Identifying a scroll is different from deciphering a scroll and neither requires expending the scroll.
Identifying
The detect magic spell determines if there're any magic auras in the area on the first round, the number of magic auras and the most potent aura in the area on the second, and where exactly those auras are and how powerful each is on the third. With a successful Knowledge (arcana) skill check (DC 15 + spell level), the caster can determine the aura's school of magic; this check apparently takes no time and is part of the 3rd-round detect magic effect. Doing this would tell the caster only the school of the spell or spells on the scroll.
A 3-round thorough examination of the object while employing the detect magic spell permits the caster to "[i]dentify the properties of a magic item" with a successful Spellcraft check (DC 15 + scroll's caster level). This tells the caster everything about the magic item, with apparently one exception. The caster knows whether the scroll is arcane or divine, what level spell is on it, what level the spell or spells are scribed at, and so on, but identifying doesn't reveal exactly what spell is on the scroll; to do that the caster must decipher the scroll.
These 3 rounds are in addition to the first 3 rounds leading to pinpointing each aura in the area of the spell detect magic. Events happen in order unless stated to happen simultaneously.
(The analyze dweomer spell also reveals these properties, but the word dweomer is difficult to say without laughing.)
Deciphering
To find out which spell is on the scroll (and subsequently be able to activate it) the caster must decipher the scroll, which requires a successful full-round Spellcraft skill check (DC 20 + spell level), a successful 1-minute Use Magic Device skill check (DC 25 + spell level), or the read magic spell.
After the scroll's deciphered, that scroll's always deciphered for that caster. No further checks need be made, and the scroll can be employed normally.
Don't conflate identifying with deciphering. The hairs are fine and difficult to split but the game splits them anyway: When a caster identifies an item's properties, he gets command words, number of charges, and so on (pretty much just like he read the item's description from the book) but not the name of the spell on the scroll; the caster gets that and the ability to activate the scroll from deciphering the scroll.
Note: That's weird and the Pathfinder Role-playing Game buries that on page 490: "The writing on a scroll must be deciphered before a character can... know exactly what spell it contains." This also isn't exclusive to Pathfinder--both the Dungeons and Dragons 3.0 and 3.5 Dungeon Master's Guides have the exact same language in their Deciphering a Scroll sections (pages 203 and 238, respectively).
Note: A solid but dangerous case can be made for skipping the identification step if the caster already knows what he's dealing with, much in the same way someone proficient with a sword can just whack fools with the sword instead of learning its maker, properties, and history before he starts using it. The DM rolls secretly to determine if a character deciphers gibberish via the Linguistics skill, but the player rolls openly to decipher a magic scroll via the Spellcraft skill or Use Magic Device skill, so right there the player will know it's a magic scroll and, if successful in deciphering it, know the spell on it. The character can then try to activate the scroll, but--and this is really a DM's call--the character still won't know any of the scroll's properties (such as it's spell level or the scriber's caster level) because the character's not identified the scroll's properties. Just as Fighter Joe can still take swings with a magic sword without knowing its exact properties, Wizard Jim can decipher a scroll and, if he meets the requirements, cast the spell from the scroll without knowing exactly what's going to happen. I've never seen a player want to do that, but I'd totally let him. That could be hilarious.
Other Tidbits: There are spells that straight-up answer questions and get information; one could possibly use those and make a big pile of information about a scroll. There are feats and classes that are scroll-specific, and those might be useful. I've ignored both because they seem to be beyond the question's scope.
No, detect magic doesn't automatically detect spellcasters as magical
The Sage Advice Compendium addresses a related question:
Is the breath weapon of a dragon magical?
If you cast antimagic field, don armor of invulnerability, or use another feature of the game that protects against magical or non-magical effects, you might ask yourself, “Will this protect me against a dragon’s breath?” The breath weapon of a typical dragon isn’t considered magical, so antimagic field won’t help you but armor of invulnerability will.
You might be thinking, “Dragons seem pretty magical to me.” And yes, they are extraordinary! Their description even says they’re magical. But our game makes a distinction between two types of magic:
- the background magic that is part of the D&D multiverse’s physics and
the physiology of many D&D creatures
- the concentrated magical energy that is contained in a magic item or
channeled to create a spell or other focused magical effect
In D&D, the first type of magic is part of nature. It is no more dispellable than the wind. A monster like a dragon exists because of that magic-enhanced nature. The second type of magic is what the rules are concerned about. When a rule refers to something being magical, it’s referring to that second type. Determining whether a game feature is magical is straightforward. Ask yourself these questions about the feature:
- Is it a magic item?
- Is it a spell? Or does it let you create the effects of a spell that’s
mentioned in its description?
- Is it a spell attack?
- Is it fueled by the use of spell slots?
- Does its description say it’s magical?
If your answer to any of those questions is yes, the feature is magical.
Let’s look at a white dragon’s Cold Breath and ask ourselves those questions. First, Cold Breath isn’t a magic item. Second, its description mentions no spell. Third, it’s not a spell attack. Fourth, the word “magical” appears nowhere in its description. Our conclusion: Cold Breath is not considered a magical game effect, even though we know that dragons are amazing, supernatural beings.
Detect magic, like other game mechanics, operates by this same logic with regard to what is considered magical. The spellcasting abilities of creatures (innate or otherwise) are considered "the background magic that is part of [...] the physiology of many D&D creatures". Detect magic is designed to detect magical effects, not the background magic that suffuses creatures or the universe.
Chris Perkins confirms this sort of interpretation here:
Can detect magic detect magic potential of spellcasters even if they're not actively casting a spell?
It's not a wizard detector, if that's what you mean.
Given that the question he's responding to asks about spellcasters in general, it seems clear that his response is not specific to wizards - he's suggesting that the spell doesn't automatically detect spellcasters simply due to their magical abilities.
Best Answer
No, there's no difference. Detect magic would say if there was. Both types can detect the other's magic equally well.
Technically, not the even the different Knowledge skills apply to detecting magic itself. They apply to identifying the results of the two different kinds of magic, though, based on which one creates them most commonly - undead fall into Religion while constructs fall into Arcana. Note that this part isn't straightforward either; both kinds can summon outsiders (Know: Planes) and animals/magical beasts (Nature; which is associated with divine casters specifically through the Druid and Ranger).
For identifying actual spells, either as they are cast or by studying their ongoing effects with detect magic (and identifying magic items with either detect magic or identify), you use the Spellcraft skill. This doesn't change regardless of your or the other caster's traditions. Note that many spells that at first glance clearly belong on one side or the other quickly get mixed up when classes besides wizard and cleric get added to the mix.