All molecules express by the immune system are widely studied nowadays. The international identification of molecules express on the surface of a leukocyte need to be univocal and clear, thus an international naming system has been developed (protocol). All the molecules can have more than one name but definetily they will only have a specific CD identifier.
For example the lymphocyte function-associated antigen 1 is referred to as LFA1, alphaL-Beta2 or CD11a/CD18. As you can see this particular molecule is a dimer i.e. made up of 2 protein CD11a and CD18 and because there are more than one member of the CD11 family (CD11a to d) they are followed by the letter to distinguished between them.
In short CD is just an internationally recognized scientific system to name a single molecule.

For the function part I would not consider that to be truthful. There are so many CD molecules with so many functions and yes some will be Receptors express on one cell type and they can be use to bind to other molecules expressed on "target cells" (thus they are called ligands) but not all of them will function like this. For an example LFA1 binds to ICAM1 (also known as CD54) and other related molecules. Usually the ligation between a receptor and its ligand induce activation of a signaling pathway leading to some functional outcome.