Different kinds of ellipsis have different identity conditions (aka isomorphism conditions): Some are more syntactic while others are more semantic in nature.
Roughly, this gradience corresponds to how plausible it is that the ellipsis is built in the syntax but is deleted at PF – or that it is just a piece of content encoded in a null proform (catchphrase what you see is what you get).
Try to rank the five 'kinds' • Nominal ellipsis, • Gapping and Stripping, • Sluicing, • VP ellipsis and • Null Complement Anaphora along the cline from syntactic to semantic, in a partial order!
Connect with the influential distinction between 'deep' and 'surface' anaphora made by Hankamer and Sag (1976) (Deep and surface anaphora) – for relativizations, see Kehler (2018) (Ellipsis and Discourse).