What is the difference between molecular weight and molar weight

Molecular weight the weight of a molecule.

Molar weight is the weight of a mole.

But I'm surprised that you are referring to 'weight' instead of mass... :confused:

The MOLECULAR WEIGHT of a compound is the total weight of all the atoms comprising a molecule of that compound. The units are amu (atomic mass units). We are talking about a single molecule. If we have an individual atom - a Xenon atom, for instance - we should speak of the Atomic Weight; if we are considering an ionic compound - Sodium Chloride - we should refer to it's Formula Weight.
The MOLAR WEIGHT is the weight of a mole of the compound, We are almost always talking of GRAM MOLES which is simply the molecular weight expressed in grams - the easiest conversion in Chemistry! (Many times I have calculated pound moles for the engineers, they work in english units.) An mole has the same number of units as a mole of something else. Just like dozens - a dozen of this is the same number as a dozen of that.
A gram mole, of course has an Avogadro's number of things. 6.02 x 10^23 things. But we can't count them individually -- too many, and we can't even find them -- too small, so we use the mole concept and count them by weighing them.