In every game I've ever played or judged, magical traps will radiate magic unless they're hidden by an undetectable aura spell. And in that case the caster gets a caster level check to see if he discerns the hidden aura.
However, that's not the same as "finding a trap"--that requires the search skill.
If a PC detects magic on a door using detect magic, they'll find out that there are two auras on the door: both of which are weak abjuration magic. That could be lots of things--two Arcane lock spells, an Arcane Lock spell and an Alarm spell, or some kind of glyph. The PC could try to dispel the magic. If they think it's a trap, they could try to guess what it was and take precautions (Spell Resistance, Protection From Elements, etc). However, the PCs don't know for sure that either of them are traps. And they haven't "found" the traps so, even if they have ranks in disable device (which is quite possible for a wizard) and would be able to help disable the trap if someone figured out where it was.
On the other hand, a rogue could search the door and find out whether or not there is a trap. If the rogue finds the trap, he'll know more or less what it is, what triggers it, and what it does. (Not so for the detect magic user. If an embedded fireball spell on the door is triggered to go off when the door opened inward instead of outward, he won't know--the rogue will). Note that the rogue can do this without using a spell and that the search check takes the rogue 1 round instead of three rounds of concentration for the wizard to get useful information. The rogue also will be able to attempt to disable the trap--magical or otherwise.