A ligand gated channel is an ion channel in a cell's membrane that is opened or closed by the direct binding of a chemical messenger. It allows the passage of certain ions back and forth across the cell membrane as a direct result of a specific substance binding to it. These specific substances are neurotransmitters; they stimulate the opening and closing by transmission osf nervous impulses.
A G-protein channel is an ion channel also, but it differs in that it is associated with a specific family of proteins it will allow transport back and forth across the cell membrane. This one is kind of like "What's the password?" You have to have a membership card, you have to be in the club to gain admittance.
The second messenger system contrasts largely with the ligand gated channel in that it is an indirect influence. The specific substance binds to receptor sites on the cell's membrane surface. These receptor sites in turn target specific molecules within the cell's cytoplasm, in the interior of the cell. A good example here would be the production of epinephrine, which produces the "fight or flight" response in organisms.