I am completely confused about why molar mass is the same as atomic mass. Could someone help explain why, thoroughly, but in simplified terms?
Ar - relative atomic mass is the ratio of the mass of one atom of an element to 1/12 of the mass of one atom Carbon-12 which has Ar of exactly 12. It is a dimensionless quantity. The Ar values are what you see in the periodic table, reflecting the isotopic compositions of the elements (that's why Ar(C)=12.011 and not 12).
Mr - relative molecular mass - ratio of the mass of a molecule to 1/12 of the mass of one atom Carbon-12. As with Ar, Mr is also a dimensionless quantity. It can be calculated as the sum of the relative atomic masses of the constituent elements.
M - molar mass - this is the mass of a substance (m) divided by the amount of substance (n) and therefore has units of g/mol. I can be calculated as Ar (for atoms) or Mr (for molecules) multiplied by 1 g/mol (also called the molar mass constant or standard molar mass) to ensure units of g/mol.