Would a Ring of Wizardry combined with the Alternative Spell Source Feat allow a Diving Caster to increase prepared spells

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.

• Samsaran race with Mystic Past Life alternate racial trait lets you learn a few off-list spells. They must match your actual class in arcane/divine type, but are otherwise unrestricted. Lightning Bolt exists as a divine spell via the Adept class, so it's a valid choice.

• Page of Spell Knowledge adds any one spell to any caster class. It's supposed to require spontaneous casting, and supposed to only apply to spells that are already on your class list... but those are just prereqs for using a magic item, so you can spoof them with UMD.

• Lightning subdomain has Lightning Bolt. However, your limited number of domain spell-slots make this not great for a heavy specialization, unless you also import the Domain Spontaneity feat from 3.5e.

• Dreamed Secrets lets a divine caster learn Wizard spells. However, it's not appropriate for spells you plan to specialize in, since you can't cast them reliably; it takes a Will save (DC 20) each time you try.