Ionotropic receptors are transmembrane molecules that can open or close a channel that would allow smaller particles to come in or out of a cell. The name gives this clue, but an “ionotropic” receptor allows ions to travel in and out. They are not always open; they are usually closed until a ligand or neurotransmitter binds to the receptor.
Metabotropic receptors do not open or close. They are instead linked to a small chemical called a “G-protein.” As soon as a ligand bind to this kind of receptor, it activates the G-protein, which then activates another molecule. That next molecule is called a “secondary messenger.”