Mass
The basic SI unit of mass is the kilogram (kg). In physics, mass is not the same as weight, even though mass is often determined by measuring the object's weight using a spring scale, rather than balance scale comparing it directly with known masses. An object on the Moon would weigh less than it does on Earth because of the lower gravity, but it would still have the same mass. This is because weight is a force, while mass is the property that (along with gravity) determines the strength of this force.
Molar mass
While molar masses are almost always, in practice, calculated from atomic weights, they can also be measured in certain cases. Such measurements are much less precise than modern mass spectrometric measurements of atomic weights and molecular masses, and are of mostly historical interest. All of the procedures rely on colligative properties, and any dissociation of the compound must be taken into account.