What are the differences between a grab and a command grab?
The specific meaning is probably dependent on which game you're talking about. When it comes to fighting games, I've only gone deeply into one, and that's Smash Bros.
In Smash Bros, a normal grab is executed by pressing r1. This grab goes through sheilds, but it's generally slower than most attacks and if the enemy attacks while you're grabbing, their attack hitbox takes precedence over your grab, so they win that exchange.
Command Grabs in smash bros are available to some characters as a special attack (with the B button). Like normal grabs, they usually (but not always) go through shields. Often they have more range than a normal grab, but more startup time, and they often don't give you options about what to do when you've grabbed someone -- the rest of the attack is decided for you if you land the grab. With normal grabs, in contast, you can choose to throw them up, down, to the side or not at all. Usually not with command grabs (I believe there are exceptions to this).
So yeah, in Smash Bros a command grab is a special attack that has some properties of a normal grab, but some differences.