Basically, both meteor smashes and spikes(aka pure meteor smashes) are moves that hit you downwards, just like Captain Falcon's down air, Donkey kong's forward air and Lucas' back air.
Now, the difference between a spike and a meteor smash is that you can cancel your downwards momentum after being hit by a meteor smash by jumping/using up b. A spike, on the other hand, will just force you to take the entire trip down before you can start recovering(IF you survive, that is).
I believe there's only one spike in Brawl, namely Luigi's taunt, every other move is a meteor smash if i remember correctly(correct me if I'm wrong).
In Melee there are a couple more, like Falco's down air.
What you should know about the competitive aspects of meteor smashes is to always try to meteor cancel(jump when you're being struck down).
There's a timing to it, of course; you'll need to wait for half of the hitstun to pass before you can try jumping iirc.
It's a situational survival tool