Paizo has studiously avoided publishing a single official word on psionics. The only psionics rules are from a third party, Dreamscarred Press, but are in the online Pathfinder SRD. According to those rules, if you are using magic-psionics transparency, then you treat powers just like spells or spell-like abilities, so yes, detect magic would detect and identify them. The question reduces to "How does that work with a spell-like ability?" Transparency means "the same" so yes. Spellcraft would let you ID a power as it was being used; Detect Magic would identify an active power's school (note those are two different things). If you use magic-psi transparency then psi is magic and all the same rules apply.
They include the separate PsiCraft skill because you don't have to use "magic-psionics transparency". That's just the default. A GM could, if they wanted, make them opaque to each other, at which point a Psicraft skill is necessary. Also because some classes might have Psicraft as a class skill that don't have Spellcraft.