You need to restart the process of acquiring ritual spells via this mechanic.
The process of copying the spell into your ritual book takes 2 hours
per level of the spell, and costs 50 gp per level.
The feat mentions this.
When you choose this feat, you acquire a ritual book holding two
1st-level spells of your choice
This occurs only when you choose the feat.
Afterwards the content of the book, a physical object, is governed by the process described above. So if you lose it, your only recourse is to find more spells and use the rule above to scribe rituals into a new book.
As a general comment, the gist of the game is for the referee to present a setting for the player to experience as their character. In this sense it is a pen & paper virtual reality. This relates to your question in that given the lack of specific rules, you should consider the issue as if you were really there. The Warlock getting his Book of Shadows (PHB 108) is an example of a specific exception to the assumption of a pen & paper virtual reality. In this case the character has a physical book filled with ritual spells. Lose the book and you lose the spells and have to spend time and money to make a new one.
Note that there appears to be no initial cost assigned to making a new ritual book. However, in the equipment list a spellbooks cost 50 gp, and a blank book 25 gp. Personally, I would charge a PC the spellbook cost for a new ritual book. However, if you are not comfortable with that then charge the player the cost of a book. Other than that, there is nothing to prohibit characters from spending additional time and money to make a backup book.
Also, this is consistent with how the Wizard spell book works on page 114, which is the closet relevant mechanic.
Of interest is that the ritual feat is the only way for a sorcerer to cast ritual spells, as he doesn't possess a ritual casting feature as a function of class as far as I can tell.
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
Yes, spell scrolls are always destroyed by copying. From the DMG entry on spell scrolls, page 200:
(Emphasis mine.)