It's pretty much that simple. In my opinion, BJTs are more applicable for linear amplification circuits.. take something and make it bigger (in this case, current.) FETs are ideal as switches. They'll both do either, but their characteristics lend themselves to applications. Some will disagree.
On a FET, you need to provide enough voltage to get it switched fully on. The spec sheet will list Rds(on) at a particular voltage. You want to provide the voltage listed in this spec, not the Vgs(thresh) spec. That's where it's just beginning to turn on.
On LEDs.. the current defines brightness. More current, brighter. Less current, dimmer -- and cooler. 
Nothing special there really.