Is molecular mass and molar mass the same?

Yes, they are. The terms gram molecular mass/atomic mass and molar mass are used interchangeably.
Gram molecular mass is the mass of one mole of a given molecular compound with units specifically in grams, and it is equal to the sum of atomic masses of all constituting atoms in said compound.
The term molar mass is gram molecular mass, BUT molar mass can also be used in place of gram atomic mass, or even gram formula mass (when dealing with ionic compounds.)
Let’s examine the molecular mass in grams (or you could say the molar mass) of ##CO_2## (carbon dioxide.)
##CO_2## is a molecule with one carbon atom and 2 oxygen atoms.
(atomic mass of carbon) ##+## ##2*##(atomic mass of oxygen) ##=## molecular mass of carbon dioxide

atomic mass of carbon is 12 ##(g)/(mol)##

atomic mass of oxygen is 16 ##(g)/(mol)##
##:.## molecular mass of ##CO_2## is
##12(g)/(mol)+2*16(g)/(mol)##
##=44(g)/(mol)##