Remote head key
One moulded piece: a cut blade, a transponder and the lock and unlock buttons all in the same head. Break the buttons and you still have a key that works in the door and ignition.
Replacing one means supplying the whole unit and cutting the blade to match yours.
Separate remote
A plain mechanical key, with a plastic remote riding alongside it on the ring. The two are independent, which is convenient: a dead remote does not cost you a key.
Often the cheapest of the three to put right, because the remote can be replaced without touching the key.
Smart or proximity key
No blade you use day to day. The car detects the key nearby and unlocks or starts on a button. Almost all of them hide a small hidden mechanical blade inside the fob, and a matching lock somewhere on the door.
Worth finding that hidden mechanical blade before you need it, rather than the day the fob battery dies in a car park.