The key difference between back bonding and coordinate bonding is that back bonding refers to a chemical bond that forms between an atomic orbital of one atom and an antibonding orbital of a ligand whereas coordinate bonding refers to the sharing of a pair of electrons between an electronegative species and an electro-deficient species.
Coordinate bonds commonly occur in coordination complexes in which a central metal atom is surrounded by a set of ligands, which are bonded to the metal atom through coordinate bonds. Here, the ligands share their lone electron pairs with the metal atom. But, in back bonding, a chemical bond forms between an atomic orbital of one atom and an antibonding orbital of another atom when they have equivalent symmetries. In organometallic chemistry, this type of chemical bonds is common.
