There's technically three types of powers in Mass Effect: Active Powers, Grenades and Passive Abilities.
Active powers a single Global Cooldown. A skill either activates the Global Cooldown or it doesn't. Skills that don't activate a cooldown are only limited by how quickly you can perform the action (the time it takes to switch ammo/throw a grenade).
Most powers listed as a base power here qualify as Active. These are your standard attacks and always cause a cooldown.
Passive powers are always active and don't have cooldowns, simple enough. Ammo powers are technically passive, and you can always switch ammo regardless of cooldown. Tech Armor is basically a passive power unless you detonate it.
Grenades don't use a cooldown either, and if something seems like an "active" power and it doesn't activate the cooldown, that's because it's technically a grenade. Proximity mines, Nova and Sentry Turrets are all technically grenades.
Nova has a "cooldown" that's actually based on your Biotic Barrier (the purple "shield" Vanguards have). You can't use Nova if your Biotic Barrier is empty, but it otherwise ignores cooldowns like a grenade.