Antigenic and non antigenic
Something is antigenic because it acts as an antigen - it binds to an antigen receptor in the immune system (antibody, B-cell receptor, T-cell receptor, etc.). While the concept of "foreign" in immunology is often (incorrectly) equated with antigen, that is not the case. For example, there are many chemicals one could think of that are foreign (non-self), but don't usually raise immune responses - nylon, for example.

The difference between an antigenic and non-antigenic peptide is that the antigenic peptide, when presented in the correct circumstances, can raise an immune response. This means that, theoretically, the exact same peptide sequence can be both antigenic and non-antigenic depending on the environment - whether it's being presented in an immune-suppressed environment, for example. However, it's more common to classify antigenic potential based on whether it's possible for the substance to raise a response in an otherwise "normal" immune environment.