Mass-effect – Does the color of the shield mean anything

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.

There are definite synergies between various classes and certain weapon types. First of all, many powers and abilities only work with specific weapons, or give special bonuses when used with specific weapons. For instance, Vanguards have access to a number of bonuses to Shotgun damage, and Soldiers have access to several Assault Rifle upgrades. Infiltrators have access to lots of Sniper Rifle synergies.

Additionally, only Soldiers and Infiltrators experience the 'time dilation' effect when looking down the scope of a Sniper Rifle - this is invaluable for setting up headshots.

Finally, different classes have different weight allowances. Because some weapon types - notably Assault Rifles and Sniper Rifles - are much heavier than others, trying to carry one with a class with a low weight capacity (like an Adept) will result in a large penalty to your power recharge times. This is an important tradeoff, since these classes essentially live and die by effective use of their powers.

TL;DR: While you aren't required to use certain weapon types, there are definite rewards for specializing in something suited to the combat style of your class.