character-advancementclass-featurednd-5espellswizard
In D&D 5E Wizards get an additional two spells per level to add to their spellbook:
Each time you gain a wizard level, you can add two wizard spells of your choice to your spellbook.
If a Wizard has a handful of Scrolls and another Wizard's spellbook they have found while adventuring, can they attempt to scribe them all (assuming they are of the necessary spell level and have the time and money to do so), or are they limited to 2 new spells per level?
The rules for getting spells into wizard's spellbook are convoluted and finicky. They're summarized below so the player knows what he's getting into when he writes Wiz1 on his character sheet.
A wizard's spellbook for free initially contains all 0th-level spells and additional spells he knows due to being a level 1 wizard, usually 1st-level spells totaling 3 + the wizard's Intelligence modifier. Some 0th-level wizard spells were published after the Player's Handbook; ask the DM if these, too, are included in a new wizard's spellbook, if the wizard picks 19 0th-level spells (the number of 0th-level Player's Handbook wizard spells), or if the DM has another system. At each new wizard level the wizard adds 2 new spells to his spellbook. This is free and takes no time.
Many prestige classes technically eliminate these free level-up spells. An extremely common house instead has such prestige classes grant these free spells upon gaining a level anyway but ask the DM.
The wizard takes 1 day to study a scroll or another wizard's spellbook and makes a Spellcraft skill check (DC 15 + spell level). Success means the wizard can add the spell to the wizard's spellbook. Failure means the wizard "cannot attempt to learn or copy that spell again until [the wizard] gains another rank in Spellcraft" (PH 179). Ask the DM whether this means the spell can't be learned from this source or if the spell can't be learned from any source. It might be important.
The wizard then takes 1 day to copy the spell into a spellbook. A spell occupies 1 page per spell level (minimum 1 page) and costs 100 gp per page. Copying a spell from a scroll deletes the spell from the scroll, but copying a spell from another wizard's spellbook leaves the other spellbook intact. The wizard can also copy a spell the wizard's prepared; when finished, the spell is gone as though cast.
If the wizard has a spellbook, he can duplicate that spellbook by taking 1 day per 2 spells and spending 50 gp per occupied page.
This can be very cheap--free, even--but, obviously, dangerous. After acquiring another wizard's spellbook, the wizard attempts to attune to it (Complete Arcane 140). Instead of using the rules for preparing a spell from another wizard's borrowed spellbook (PH 178), the wizard makes a Spellcraft skill check (DC 25 + the level of the highest-level spell in the spellbook) and takes 1 week plus 1 day per spell. Success means never again needing to make a Spellcraft skill check to prepare spells from that spellbook.
The wizard alternative class feature eidetic spellcaster (Dragon #357 89) eliminates the wizard's familiar but grants the wizard the ability to prepare spells, know spells from leveling up, and know spells learned from other's spellbooks (scrolls go unmentioned) without needing a spellbook at all. Costs are still incurred for learning new spells (e.g. the fee another wizard charges for access to his spellbook), but other costs just aren't. (Actually, the text says a wizard with the eidetic spellcaster alternative class feature "must pay all the normal costs for learning new spells (used instead in special incenses rather than inks) but [the wizard does] not need to put [the spells] into a spellbook," but there is no normal cost for learning a spell.)
(It's possible--even likely given the parenthetical--that the author of the eidetic spellcaster alternative class feature intended the standard cost for putting a spell into a spellbook still be paid (albeit only once forever) to add a spell to the character's virtual mental spellbook. Pitching such a requirement might mollify an otherwise wary DM. Never losing one's spellbooks and--barring ridiculous tragedy--never needing a backup might be worth a familiar in some campaigns, even given the expense. Further, other options exist for storing spells differently using feats, alternative class feature, substitution levels, and non-books as equivalents to spellbooks. This one's probably just the best.)
Using the 3rd-level Sor/Wiz spell secret page [illus] (PH 275) to make a 1-page-long yet extremely deep spellbook is frowned upon by many DMs and considered outright cheese by many players. I present it here without judgment. The spell secret page says that it
alters the contents of a page so that [the contents] appear to be something entirely different. [...] The text of a spell can be changed to show a ledger page or even another spell. [...] You are able to reveal the original contents by speaking a special word. You can then peruse the actual page, and return it to its secret page form at will.
At least one source, Frank and K's online Dungeonomicon, pitches the spell secret page as the wizard's primary spellbook management tool. The wizard casts the spell secret page, touches a page, and a spell's text is the new visible layer, concealing whatever's beneath it, perhaps even previous castings of the spell secret page depending on how the DM rules the spell interacts with Combining Magical Effects (PH 171-2). Spellbook duplication this way is cheap and easy, but possibly still time consuming depending on the wizard's available resources.
There are a multitude of reasons even a generous DM may forbid this practice, and at least one reason (the 3rd-level Sor/Wiz spell dispel magic [abjur] (PH 223) et al.) a paranoid wizard would avoid this practice. Nonetheless, its advantages are huge, but a wizard player shouldn't surprise the DM with his wizard character's secret page spellbook in the middle of session and expect favorable treatment. Talk to the DM first and see if he agrees wizarding is overpriced, and if so then pitch the spell secret page as an alternative.
The held item Boccob's blessed book (DMG 249) (12,500 gp; 1 lb.) is a lockable (how lockable goes unmentioned), waterproof 1,000-page spellbook that permits transcribing spells to it without expending 100 gp in materials per page. If a wizard's fills a blessed book, he's saved 100,000 gp by spending 12,500 gp (or by spending half that if the wizard made it himself... by using the spell secret page, see above). This is the typical wizard's go-to for reduction of spellbook costs.
(The feat Ancestral Relic (Book of Exalted Deeds 39) gives a wizard means both to ditch at full price Greyhawked items (e.g. leftover kobold spears, oversized or undersized suits of armor, unwanted magic items, Maure Castle flooring) and to beef up the protections on or utility value of his spellbook, perhaps allowing a little extra cash for scribing.)
TL;DR: Spell scroll is a consumable item. It holds a spell which can be cast from it or copied into a wizard's spellbook, both of which destroy the scroll. Spell on a scroll refers to that specific spell, which is incidentally written on a scroll.
Spell scrolls (as you'd find in the treasure tables) are spells already prepared onto the scroll and contain some/all of the magic needed to cast them within them (which is why creating them is more than just copying things out of a book).
The second passage you are quoting describes how wizards copy any spell that they find written on a piece of parchment, in a book or on the back of a box of your favourite Orcish breakfast cereal, and put it into their spellbook.
Copying a Spell into the Book. When you find a wizard spell of 1st level or highter, you can add it to your spellbook if its of a level for which you have spell slots and if you can spare the time to decipher and copy it.
Copying a spell into your spellbook involves reproducing the basic form of the spell, then deciphering the unique system of notation used by the wizard who wrote it. You must practice the spell until you understand the sounds or gestures required, then transcribe it into your spellbook using your own notation.
The rules in the DMG are specifically about spells on spell scrolls (the type found in the random treasure tables etc.)
In addition to the rules on copying any spell into your spellbook you also have to follow these rules specific to spell scrolls.
A wizard spell on a spell scroll can be copied just as spells in a spellbook can be copied. When a spell is copied from a spell scroll, the copier must succeed on an Intelligence(Arcana) check with a DC equal to 10 + the spell's level. If the check succeeds, the spell is successfully copied. Whether the check succeeds or fails, the spell scroll is destroyed.
Basically you get one shot to understand enough about this spell scroll before the magic is used up and you can't copy it into your book.
So yes, there's a difference between a plain written spell on any old piece of parchment, and a spell scroll.
Additionally: As KorvinStarmast brought up in the comments you could have someone else help you with this check using the Help action.
Help
You can lend aid to another creature in the completion of a task. When you take the Help action, the creature you aid gains advantage on the next ability check it makes to perform the task you are helping with, provided that it makes the check before the start of your next turn.
Bare in mind that many DMs rule that you can only help with tasks that it makes sense for you to be able to aid someone with. In this instance I would think that at the very least they'd need to have the spell in question on their own class's spell list, or perhaps even be a wizard themselves.
Best Answer
Copied spells and the two free spells are separate
Note the full wording1 of the Learning Spells of 1st Level and Higher section (emphasis mine):
There is a clear distinction here. Whenever you gain a level, you get two free spells. Separately, you might add other spells to your spellbook, as detailed in the spellbook sidebar. These are two separate methods of getting additional spells for your spellbook.
So if you have scrolls or another spellbook, you can copy any of those spells following the costly copying method, independently from the free spells obtained at level up.
1. Apparently some older versions of the PHB did not have "for free" at the end of the first sentence of the quote. It seems to have been added silently (without being noted in the errata docs), according to Someone_Evil.