How are moles of different elements/compounds the same? how are they different?

A mol is the number of atoms or molecules it takes to make up the the atomic mass (just think "weight" for now) or molecular mass/weight in grams.  E.g., since the atomic weight of oxygen is 16, the "gram atomic weight" of oxygen is 16 grams.  It will "turn out" that it is the same number of atoms needed to make up 16 grams of oxygen as make up 12 grams of carbon or 1 gram of hydrogen, or "N" grams of any element with molecular weight "N".