L21 and C1b refer to the cubic crystal structures of "full" heusler alloys (X2YZ) and "half" heusler alloys (XYZ). The actual space groups of the two are Fm-3m (225) and F-43m (216).
The names come from an old nomenclature system. For example simple single element FCC is the A1 structure and BCC is the A2 structure and so on (there are many). An ordered 1:1 FCC structure is B1 (rock salt structure) and ordered BCC is B2 etc etc.
Not a great deal of information is imparted by this naming system, but it is useful to know what someone is talking about if they use it. I found this page with a number of examples on it:
In crystallography, L21 refers to a typical structure of X2YZ type designated according to struckturbericht nomenclature where Y and Z atoms occupy interpenetrating FCC positions and X2 atoms occupy tetrahedral positions symmetrically in the cubic structure.