“Atomic mass” is relative to the isotope carbon-12 weighing exactly 12 atomic mass units. Therefore “atomic mass” is precisely the same as “relative atomic mass.”
Two further points:
First, atomic mass as stated on the periodic table is a average of the masses of an element’s naturally-occurring isotopes, weighted by their abundance. This is because atomic mass as normally used is a bulk property: we weigh out many trillions of atoms at a time, because we usually deal in macroscopic quantities. And that means that an average mass is more useful to us.
Second, all masses are relative masses (until the new, physical-constant-based kilogram comes online; and arguably even then). We mass something by comparing it to some standard of reference: until later this year, that something is a chunk of alloy in Paris, France. When the new standard comes into use, we will be comparing the kilogram’s gravitational mass to the strength of the electromagnetic force.
But that’s kind of trivial; it just stems from the fact that any and every measurement is a comparison to something else.
Edit: IUPAC, the world’s premier organization for the imposition of picky definitions that most people never need to use, has the following:
Atomic mass is the mass of a single atom; the unit is the Dalton or unified atomic mass unit. (I would use “isotopic mass” to specify the mass of a particular atom, but that’s not sanctioned by IUPAC.)
Relative atomic mass is the measured average mass of all atoms of a particular element in a particular sample. To make it unitless, it’s divided by the value of the unified atomic mass unit.
Standard atomic weight is the value you read off of the periodic table; it’s an Earth-based average over many samples, of experimental values of the relative atomic mass. Values are promulgated by the IUPAC Commission on Atomic Weights and Isotopic Abundances, and are revised every two years.
Most chemists refer to standard atomic weight as “atomic mass” or “atomic weight” and get on with their lives.
The unified atomic mass unit is 1/12 of the mass of an atom of carbon-12. It is sometimes called the Dalton.
Definitions taken from the IUPAC Gold Book.
As far as I can tell, relative atomic masses and standard atomic weights are made unitless so that they can be used with any convenient macroscopic mass unit to determine correct proportions for a desired chemical reaction.