This makes it sounds like a wizard would have a really hard time to prepare a spell from another's spellbook. Is that the case?
That is correct.
As you quoted, each wizard's spellbook notation is unique, therefore you can't prepare spells from someone else's book.
You must first copy the spell into your own book (deciphering the notation in the process), after which you can prepare it as normal.
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
First off, there's going to be a lot of variation here. Not all adventures have opportunities to access a spellbook, so you're likely to see whole campaigns where it never comes up and others where they're everywhere.
Lets look at some examples though, from various seasons of Adventurers League, just out of curiosity.
Season 1: 6 spell scrolls from the tier 1 adventures, most of which are on the Wizard spell list, and thus could theoretically be copied into a spellbook. In the 5 tier 2 adventures every single one of them has a spellbook or two that the players can theoretically get access to. There are also several scrolls. Apparently the authors went spellbook happy in the Tier 2 parts of this season.
Season 2: The tier 1 adventures have a handful of scrolls and 2 spellbooks. The Tier 2 adventures have a handful of scrolls and 1 spellbook.
Season 3: Tier 1 has a handful of scrolls and no spellbooks. Tier 2 has a few scrolls and 2 spellbooks. Tier 3 has a few scrolls and 1 spellbook.
In each of these cases the spellbooks in question have a number of spells, some of which you could immediately copy and some of which you need to wait till you are higher level. It's also not necessarily certain that the players will get access to the spellbooks. There's also some serious overlap between stuff in each spellbook and stuff the PCs probably already know.