The two terms are not synonymous, but from a rules perspective, they are very near it. At least a few rules citations - some from your examples, and a few more I've cited below - indicates that "casting spells without preparation" qualifies as "casting spells spontaneously", but casting spontaneously isn't the same as casting spells without preparing them.
First, to clear up the part I feel is most importent: Sorcerer and bard spellcasting is "spontaneous" for the purposes of feats like in your examples. Please see the Quicken Spell feat description on page 98 of the Player's Handbook:
Special: This feat can’t be applied to any spell cast spontaneously (including sorcerer spells, bard spells, and cleric or druid spells cast spontaneously)
While the only mention of "spontaneous" in the actual Sorcerer's entry is in a lore section regarding how they start learning magic, it's pretty clear that the rules were written where "casting a spell you haven't prepared" qualifies as "casting a spell spontaneously". Other mentions include:
- The introduction to magic, page 169
- The introduction to the bard, page 26.
This section contains speculation: It's weak, but it's there. I find it very likely that when 3.0 was first being developed, they didn't have a name for it yet (and wrote up the sorcerer's class entry before coming up with a name for their casting style) - and then that wording stuck, especially to the feats and definitions when they were ported to 3.5 with little context. I find it especially telling that while Quicken Spell definitely refers to sorcerer casting as spontaneous, the glossary specifies that spontaneous casting is a cleric and druid ability. It's a recurring problem in OGL d20 games, as there is a LOT of copy-pasta to swallow - the language evolved, but the text did not, even when "updated".
I will try to get some more detail when I can get my hands on a 3.0 corebook, but as far as 3.5 is concerned: The wording has been spotty, but at least one rules reference starting with the core PHB has always suggested that a sorcerer or bard's spellcasting has always been considered spontaneous.
However, it should be noted that the terms are not transparent in the other direction. Clerics and druids do not cast spells without preparation; they must have prepared spells in order to have spells to sacrifice to power their spontaneous casting of three letter abbreviations. While this primarily only affects corner cases, this does mean the terms are not synonymous. For example, a wizard who has taken the Elemental Adept feat (and thus is capable of casting spontaneously) still doesn't qualify for the Air Bloodline feat, which requires the ability to cast without preparation.
So to conclude, while the terms can be used interchangeably to refer to sorcerer and bard spellcasting, there is a divide when referring to divine casters (as well as casters like wizards who've taken the Elemental Adept feat) that can matter in some cases. It is probably best to think of "casting without preparation" as a subset of "casting spontaneously": if you can cast a spell using a slot you didn't prepare that spell in, whether or not you prepared any spell in that slot, then you can cast spontaneously; but you have to be able to cast a spell using a slot you didn't prepare any spell in to be able to cast without preparation. So no, the terms are not synonymous, although sorcerer spellcasting is spontaneous. Casting without preparation is always casting spontaneously, but there are many cases in which casting spontaneously is not casting without preparation.
One, your stats are basically incapable of supporting any character who isn’t a pure spellcaster. For a pure spellcaster, those are pretty good stats, but for anyone else they’re painfully poor. An 8 in Constitution is putting your life in grave danger all the time. This is one of many reasons why I recommend against rolled ability scores. Have you spoken to your DM about this problem? Maybe you can convince him to allow a reroll or moving to an ability array or something.
Alternatively, you could maybe retrain as a spellcaster, but that’s not going to mesh well with your interest in archery. Bizarrely, 3.5 has very poor support for archery; basically all of the archery-related prestige classes are close to worthless, and archery requires a ton of really weak feats to get anything done (Point-Blank Shot is garbage but required for everything, Precise Shot is necessary but all it does is eliminate a painful penalty, Manyshot is incompatible with Rapid Shot, which is finally half-decent except you’ve burned four feats on a half-decent benefit!).
Finally, it’s conceivable that you might have more hope if your DM expanded that extremely-narrow field of available books. As is, all the best options I can think of for making use of that Dexterity (e.g. Crossbow Sniper, Dead Eye, Targeteer) are unavailable to you (examples are from Player’s Handbook II, Dragon Compendium, and Dragon vol. 310, respectively). And banning psionics means some very solid Wisdom-based magical-warrior options (ardent, psychic warrior, war mind) are unavailable to you. At the very least, Spell Compendium would mean that you actually have decent spells; as it is, you are literally weaker than a druid of half your level.
Anyway, taking what you’ve got as set in stone...
Sword of the Arcane Order is worthless to you because your Intelligence is a mere 10. It’s a great feat, but your stats need to be different.
This becomes a different story if your Intelligence goes up; then it’s the best feat you can take. Must-have if your DM allows you to change your stats, for instance. Assuming you are the only elf in the party, getting a special elf-only headband of intelligence as a reward for something might also do the trick, if the bonus is large enough.
Alternatively, you might ask your DM for a Wisdom-based analogue to Sword of the Arcane Order. Under normal circumstances, the requirement for Intelligence is something of a balancing factor to SotAO, but you really could use all the help you can get.
Sword of the Arcane Order does very awkwardly just... stop at 11th level. Low Intelligence, particularly if all your Intelligence comes from an item (i.e. you can’t improve it through another item) exacerbates this. That’s probably fine as most campaigns don’t go that high, and frankly I’m not sure there’s anything you can do to maintain a decent power level much past there anyway.
Order of the Bow Initiate is a complete waste of time.
Depending on how many levels you’ve burned on ranger, multiclassing to cleric or druid might be an option. Your Wisdom is very low for such classes, but even so their spells offer far more than ranger ever will.
Cleric would allow you to take Divine feats; you’ll miss Complete Champion quite a bit, but Complete Divine still has some good ones. I would strongly consider going for the Planning and Undeath domains, even though those are probably difficult to justify for your character. If you can think of any reason your character might get those, though, they would help you: you would get Extra Turning and Extend Spell, and could take Persistent Spell and Divine Metamagic (Complete Divine) in it so at least one spell a day is active all day. Divine power is a common choice but not the only option.
If you cannot justify the Undeath domain (likely), consider taking the Elf domain and asking if, since both the domain and ranger are giving you the same bonus feat, you could get Extra Turning as a bonus feat. Giving alternate bonus feats to replace duplicate bonus feats is pretty common.
A cloak of charisma will help a bit. You might even consider bumping your Charisma to 10 with your 4th-level or 8th-level ability score bump, but only do that if you don’t think you’ll reach the next bump; Wisdom is still the higher priority. In other words, Wis 14/Cha 10 is better than Wis 15/Cha 9, but Wis 16/Cha 9 is way better than Wis 15/Cha 10.
Druid would be awkward, considering that most Wild Shape forms are going to nix your archery. Sticking to primate forms might work, however; you could talk to your DM. But even allowing that, Wild Shape replaces your physical ability scores, completely wasting your Dexterity. You’d still be stronger than you are, but it would be awkward. The advantage is that it’s much less of a leap than cleric, since ranger is basically half a druid.
The divine crusader prestige class in Complete Divine also might be a solid option. It has full Base Attack Bonus, so it works out well enough for your archery, and it gets 9th-level spells in 10 levels. That’s great. The drawback is, the divine crusader’s spell list consists of exactly one domain. Choose wisely.
Unfortunately, without Spell Compendium you are quite limited here. War domain may end up being your best bet, and that’s kind of sad. Travel is another decent-ish option. You’ll also have to beg your DM to let you use Wisdom instead of Charisma.
The other class features of the divine crusader are pretty much garbage though; OK protection from electricity and acid damage, but that’s about it. It does get Weapon Specialization in its deity’s favored weapon, and requires Weapon Focus in the same, so hopefully you worship a deity that uses some kind of bow. Ask your DM if you can waive the Weapon Focus requirement if you choose the War domain; the domain grants that feat anyway, so it would be a complete waste to you.
A single level of cleric before divine crusader is also a decent idea. You could use the War domain to get into divine crusader in the first place, and Turn Undead remains very useful for Divine feats.
Sacred exorcist, also Complete Divine, can get you Turn Undead without having to dip cleric. Requires you be able to cast dismissal or dispel evil, though, which would put a harsh requirement on your domain choice.
At higher levels, dipping a single level of contemplative and/or divine oracle (both Complete Divine) can allow you to add more domains to divine crusader. That dramatically increases your spell list. Divine oracle 2 also has a very nice version of Evasion that works in all armor.
Unfortunately, those are all the options I can offer to you. If you do get additional supplements made available, Complete Champion, Player’s Handbook II, Spell Compendium, and Tome of Battle are probably your best bets. Expanded Psionics Handbook and Complete Psionic would also help. Unfortunately, it’s quite unlikely that you’ll get Dragon material, which is a shame, since it’d help.
Best Answer
I suggest handling [Initiate] feats as an extra domain, as both consist essentially of an extra mini-spell list and a special ability.
The rules for adding a domain to a Favored Soul are found in Complete Divine, page 20:
This should be even less nebulous for the Favored Soul than the spontaneous Cleric, as the Favored Soul does not have the Cleric's split method of learning spells. Both the "domain method" and the "add spells to the Cleric spell list method" should give the same result - the spells are now available as an option for the Favored Soul to select as part of their normal spells known.