Relativistic momentum is the momentum of an object, taking relativity into account. It is not relativistically invariant.
The term mass (i.e., with no qualifying adjective) has come to be used two ways in light of relativity: to mean the object's rest mass, which is the mass as we normally think of it, or to mean a relativistic mass, the mass equivalent of the object's total energy, including kinetic energy and relativistic effects. (Effectively, this potential terminology-confusion only arises due to relativity, and the difference is only for a moving object, and significant only if at relativistic speeds.)
Formulas for momentum:
relativistic momentum = γMrestV or given Mrel = γMrest, relativistic momentum = MrelV