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.
There are other arcane spellcasting classes that use spellbooks, like the magus. The alchemist has a “formula book” that works mostly the same way, and the witch has a familiar that functions like a spellbook for her.
In all of these cases, however, learning from scrolls is reserved for a class with very wizard-like spellcasting, that is, they must prepare exactly which and how many of each spell they know in advance.
As you note, the divine spellcasters who, like the wizard, prepare spells ahead of time don’t need to bother with spellbooks at all. Clerics, druids, and similar divine spellcasters can pray for any spell on their list, even one they have never seen before. In effect, you can think of the gods they pray to as being giant spellbooks that already have every spell available ready to go.
On the other side of the coin, we have spellcasters that do not have to prepare their spells ahead of time. The sorcerer is the quintessential example, but others exist, including some like the oracle that are divine (as you note). These “spontaneous” classes do not keep a spellbook or similar, and they cannot take advantage of the rules for copying a scroll into a spellbook. Scrolls, for them, can only be used as a scroll, not used to learn a spell. To learn a spell, they need the vastly more expensive page of spell knowledge, or the even more expensive ring of spell knowledge (which then does allow them limited ability to learn spells from scrolls and other sources).
The advantage to spontaneous spellcasters is that they are free to use these spells in any combination they like, up to their spells per day limit, where spellcasters that prepare have to choose exactly how many of each spell they want. However, generally speaking, the advantage of having access to so many spells is vastly superior, so clerics and druids and wizards are generally better than oracles and sorcerers and the like.
Best Answer
32 hours, six seconds
Given the time scales involved, requiring hours or days of study and work, it has to be assumed that, generally, you're scribing new spells in your downtime. In that case, the difference between a day and 24 hours is irrelevant.
However, this is not necessarily the case. Tome and Blood introduces a portable writing desk, and nothing specifically says you need peace and quiet, or rest, or an uninterrupted period of time to scribe a spellbook.
Step 1: Decipher the magical writing
According to the Spellcraft skill entry (PHB p.82), this takes a full-round action.
Step 2: Spend a day studying the spell
This takes 8 hours according to the Spellcraft skill entry. This means that "a day" in this case refers to a working day of 8 hours.
Step 3: Scribe the spell into your spellbook
This takes 24 hours. Taken literally, this means three 8-hour working days, even though I suspect the author may have meant one working day. The FAQ is silent on this and the Rules Compendium repeats "24 hours". We must therefore conclude that, unless the DM rules otherwise, it literally takes 24 hours of total work.
Nothing says that work has to be contiguous, or that the wizard needs peace and quiet, so he could of course bring his portable writing desk into a dungeon and scribe a few hours at a time between encounters. Nor does he need to be well-rested, so he can, by the rules, pull an all-nighter and get his spellbook written in one day.