Atomic mass
The atomic mass or relative isotopic mass refers to the mass of a single particle, and therefore is tied to a certain specific isotope of an element. The dimensionless standard atomic weight instead refers to the average (mathematical mean) of atomic mass values of a typical naturally-occurring mixture of isotopes for a sample of an element. Atomic mass values are thus commonly reported to many more significant figures than atomic weights. Standard atomic weight is related to atomic mass by the abundance ranking of isotopes for each element. It is usually "about" the same value as the atomic mass of the most abundant isotope, other than what looks like (but is not actually) a rounding difference.
Molecular mass
In the example above the atomic mass of carbon is given as 12.011, not 12. This is because naturally occurring carbon is a mixture of the isotopes C, C and C which have relative atomic masses of 12, 13 and 14 respectively. Moreover, the proportion of the isotopes varies between samples, so 12.011 is an average value. By contrast, there is less variation in naturally occurring hydrogen so the average atomic mass is known more precisely. The precision of the molecular mass is determined by precision of the least precise atomic mass value, in this case that of carbon. In high-resolution mass spectrometry the isotopomers CH and CH are observed as distinct molecules, with molecular masses of 16 and 17, respectively. The intensity of the mass-spectrometry peaks is proportional to the isotopic abundances in the molecular species. C H H can also be observed with molecular mass of 17.