I've been trying to resolve some edge cases with who can use which spell scrolls. As the DMG says in the Spell Scroll entry on page 200:
"If the spell is on your class's spell list, you can use an action to read the scroll and cast its spell without having to provide any of the spell's components. Otherwise, the scroll is unintelligible."
The issue here is the meaning of "class's spell list". It seems straightforward; surely a class's spell list is simply what is listed in the back of the PHB, from pages 207 to 211? But of course it isn't quite that simple, as clerics, druids and warlocks each get additional spells that aren't specified in these lists through domains, circles and patrons respectively. These class features seem to expand their personal spell lists directly. As an example, both Light domain clerics and Fiend patron warlocks can get the fireball spell, which isn't on the spell list of either class.
On page 109 of the PHB the warlock's Fiend patron Expanded Spell List literally says:
"The following spells are added to the warlock spell list for you."
Which shows that Fiend patron warlocks have fireball in their spell lists, and so should be able to use spell scrolls of fireball.
For clerics (and druids, which have almost identical phrasing), the Domain Spells class feature on PHB page 58 says:
"Each domain has a list of spells – its domain spells – that you gain at the cleric levels noted in the domain description. Once you gain a domain spell, you always have it prepared, and it doesn't count against the number of spells you can prepare each day.
If you have a domain spell that doesn't appear on the cleric spell list, the spell is nonetheless a cleric spell for you."
So for a Light domain cleric, fireball is a cleric spell. These spells don't say that they're added to the cleric spell list, but they are cleric spells. So the question becomes: Are cleric spells another name for spells which are on the cleric spell list?
To potentially shed some light on this, on PHB page 52 the cleric's Spellcasting feature says:
"You prepare the list of cleric spells that are available for you to cast, choosing from the cleric spell list. When you do so, choose a number of cleric spells equal to your Wisdom modifier + your cleric level (minimum of one spell). The spells must be of a level for which you have spell slots."
Which shows that clerics get cleric spells from the cleric spell list, so all spells on the cleric spell list must be cleric spells. But does that make all cleric spells part of your cleric spell list?
Which leads us to: Can clerics use spell scrolls for spells they receive through their Divine domains? And would this mean a Light domain cleric could use a spell scroll of fireball?
Best Answer
Yes, the wording does mean that a cleric of the Light Domain gains 'Fireball' as part of the Cleric Spell List; and here's why the wording is different. I hope the following helps explain why
The above Warlock phrasing, just as it's phrased for Wizards and other spell casting classes that gain extra spells through means of specialization, is phrased that way because each of those classes have a spell list that they must choose spells from as they level up. They do not inherently know all spells available to a Warlock. So the phrasing in this case means the fireball spell is added to the list of spells he can POTENTIALLY add to his 'Spells Known' list. For intents and purposes, those are now on his Warlock Spell List
Now enter Cleric, and the Paladin; which have very different methods of spell learning.
It must phrase it like this because Clerics and Paladins do not have to choose what spells they learn as they level. Clerics and Paladins inherently have the knowledge of every spell on their list....because we're awesome like that....and can prepare spells as needed in between long rests. If I wanted to go with cure wounds one day and then give up cure wounds to take Inflict Wounds after a long rest? I can do that freely. I have direct access to every spell available to Clerics. So when I choose Light Domain and it says the Fireball spell that isn't on my class list nonetheless becomes a cleric spell? It's now part of my knowledge of cleric spells (On my list of spells), and thus able to be utilized in scroll form since I now have the knowledge of how 'Fireball' works magically.
The only reason it doesn't say these spells are added to your spell list for you, is because it wouldn't matter in a Cleric or Paladin's case. Any spell that's on our spell list is a spell we can cast should we choose to. Any spell that's on a Warlock/Wizard/Sorcerer spell list, is a spell they can cast only if they chose it from their spell list when gaining levels.