Not anywhere near fighting game expert, but regular grabs have the fighter grab someone from only movement or standstill. Depending on the game you usually have some control on where or how you throw them. Sometimes you get a pummel.
A grab is a universal mechanic all characters have. Any character can run up and hit someone with an unblockable throw move for a bit of damage. This is the case in pretty much all fighting games because otherwise blocking would be way too strong.
Command throws are moves that function like throws, bypassing blocking and knocking the enemy down, but are character specific, requiring the input of a special move command. In general they deal big damage and/or put the opponent in a dangerous situation on wakeup, but leave you very vulnerable if you miss them.
A rarer case is something like Makoto or Yun’s command grabs, which deal little to no damage, but instead set them up to follow up with a big damage combo.
Command grab is one you have to input a command to execute. Grapplers often will have command grabs on top of the game’s vanilla grab/throw.
That’s always been my understanding at least.