A neurotransmitter is a chemical substance that is released by a nerve fiber due to the presence of nerve impulses; it transport chemical information from one nerve to the other. A receptor refers to a protein molecule that is found on the cell membranes of every cell, it functions by responding in an appropriate manner to chemical signals that are coming from outside of the cell. The relationship between the neurotransmitter and the receptor is that the neurotransmitter molecules typically bound with the appropriate receptors and bring about the expected changes in the targeted postsynaptic cell.
