Relative molecular mass or RMM is the molecular weight of an element or an compound. It is the number of times one molecule of the substance is heavier than 1/12 the mass of an atom of carbon (C12).
Gram molecular mass is the relative molecular mass expressed in grams.
Relative molecular mass
We know that relative atomic mass is a ratio and has no units while gram molecular mass and gram atomic mass are expressed in grams.
What about atomic weight or masses?
They are expressed in "amu" - atomic mass unit. Atomic Mass Unit is defined as 1/12 the mass of a carbon atom C12.
Atomic masses are not expressed as whole numbers because natural elements are mixtures of two or more isotopes. The atomic weight of chlorine is 35.43 amu. Chlorine exists as two isotopes 
in the ratio.
Therefore average atomic masses are not whole numbers.
Avogadro explained further that there are standard conditions of temperature and pressure as reference points to further deepen our understanding of behavior of gases. Chemists agreed that 273K or 0oC and 1atm pressure could be designated as standard temperature and pressure.
