1. Molecular mass gives the mass of a single molecule (it is sum of the atomic masses of the constituents present in the molecule), whereas molar mass gives the mass of one mole of a substance (mass of Avogadro number of molecules).
2. Molar mass is a measurement, which can be given to atoms, molecules or compounds. But molecular mass is only determined in the molecules. If it is the mass of an atom, a different terminology called atomic mass is used.
3. Molecular mass is a more precise number than molar mass by taking into account the isotopic composition of a molecule rather than the average isotopic distribution of many molecules.