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Page 200 of the DMG states:

If the spell is on your class's spell list you can use an action to read the scroll and cast its spell.

So if a wizard were to pick up a spell scroll containing a wizard spell, the wizard would be able to identify it.

Later in the same paragraph it also states:

Otherwise, the scroll is unintelligible.

So if the wizard were to pick up a sorcerer spell,the wizard wouldn't be able to read it.
In conclusion if the spell is on the reader's spell list then the reader would be able to identify it. ###Casting spells of levels the spellcaster doesn't have Page 200 of the DMG again:

If the spell is on your class's spell list but of a higher level than you can normally cast, you must make an ability check using your spellcasting ability to determine whether you cast it successfully. The DC equals 10 + the spell's level. On a failed check, the spell disappears from the scroll with no other effect.

So for example: If you have a 2nd level wizard who finds a spell scroll containing the spell fireball, the wizard can cast if it can pass an INT check of 13 otherwise it has no effect.

Page 200 of the DMG states:

If the spell is on your class's spell list you can use an action to read the scroll and cast its spell.

So if a wizard were to pick up a spell scroll containing a wizard spell, the wizard would be able to identify it.

Later in the same paragraph it also states:

Otherwise, the scroll is unintelligible.

So if the wizard were to pick up a sorcerer spell,the wizard wouldn't be able to read it.
In conclusion if the spell is on the reader's spell list then the reader would be able to identify it.

Casting spells of levels the spellcaster doesn't have

Page 200 of the DMG again:

If the spell is on your class's spell list but of a higher level than you can normally cast, you must make an ability check using your spellcasting ability to determine whether you cast it successfully. The DC equals 10 + the spell's level. On a failed check, the spell disappears from the scroll with no other effect.

So for example: If you have a 2nd level wizard who finds a spell scroll containing the spell fireball, the wizard can cast if it can pass an INT check of 13 otherwise it has no effect.

Page 200 of the DMG states:

If the spell is on your class's spell list you can use an action to read the scroll and cast its spell
 

So if a wizard were to pick up a spell scroll containing a wizard spell, the wizard would be able to identify it
 

Later in the same paragraph it also states:

Otherwise, the scroll is unintelligible.
 

So if the wizard were to pick up a sorcerer spell,the wizard wouldn't be able to read it.
In conclusion if the spell is on the reader's spell list then the reader would be able to identify it. ###Casting spells of levels the spellcaster doesn't have P.200 DMG :

If the spell is on your class's spell list but of a higher level than you can normally cast, you must make an ability check using your spellcasting ability to determine whether you cast it successfully. The DC equals 10 + the spell's level. On a failed check, the spell disappears from the scroll with no other effect.
 

So for example: If you have a 2nd level wizard who finds a spell scroll containing the spell fireball
The wizard can cast if it can pass an INT save of 13 otherwise it has no effect.

Page 200 of the DMG states:

If the spell is on your class's spell list you can use an action to read the scroll and cast its spell.

So if a wizard were to pick up a spell scroll containing a wizard spell, the wizard would be able to identify it.

Later in the same paragraph it also states:

Otherwise, the scroll is unintelligible.

So if the wizard were to pick up a sorcerer spell,the wizard wouldn't be able to read it.
In conclusion if the spell is on the reader's spell list then the reader would be able to identify it. ###Casting spells of levels the spellcaster doesn't have Page 200 of the DMG again:

If the spell is on your class's spell list but of a higher level than you can normally cast, you must make an ability check using your spellcasting ability to determine whether you cast it successfully. The DC equals 10 + the spell's level. On a failed check, the spell disappears from the scroll with no other effect.

So for example: If you have a 2nd level wizard who finds a spell scroll containing the spell fireball, the wizard can cast if it can pass an INT check of 13 otherwise it has no effect.

Page 200 of the DMG states:

If the spell is on your class's spell list you can use an action to read the scroll and cast its spell

So if a wizard were to pick up a spell scroll containing a wizard spell, the wizard would be able to identify it

Later in the same paragraph it also states:

Otherwise, the scroll is unintelligible.

So if the wizard were to pick up a sorcerer spell,the wizard wouldn't be able to read it.
In conclusion if the spell is on the reader's spell list then the reader would be able to identify it.

Page 200 of the DMG states:

If the spell is on your class's spell list you can use an action to read the scroll and cast its spell

So if a wizard were to pick up a spell scroll containing a wizard spell, the wizard would be able to identify it

Later in the same paragraph it also states:

Otherwise, the scroll is unintelligible.

So if the wizard were to pick up a sorcerer spell,the wizard wouldn't be able to read it.
In conclusion if the spell is on the reader's spell list then the reader would be able to identify it. ###Casting spells of levels the spellcaster doesn't have P.200 DMG :

If the spell is on your class's spell list but of a higher level than you can normally cast, you must make an ability check using your spellcasting ability to determine whether you cast it successfully. The DC equals 10 + the spell's level. On a failed check, the spell disappears from the scroll with no other effect.

So for example: If you have a 2nd level wizard who finds a spell scroll containing the spell fireball
The wizard can cast if it can pass an INT save of 13 otherwise it has no effect.