Consider the sentence:
While this assumption, on its own, is relatively innocuous, if implausible, in practice, it is supplemented by assumptions...
The 'if' here really means something more like 'but perhaps also'.
He appeared very happy, if not exuberant, at her arrival.
'if not' here means something like 'and perhaps even', as if the latter statement should be a more extreme version of the former. But it also feels like an exclusive disjunction. That is, it is one or maybe the other, but not both. On the other hand, 'if' by itself feels like both statements could be true.
I can conjure up many examples where both 'if' and 'if not' violate my above descriptions and many more which just seem malformed and awkward but fit them, e.g., 'He seems happy, if not a little confused'. or 'The proof appeared correct, if sloppily constructed,'... Adding further confusion, if I make a small change to the previous example: 'The proof appeared correct, if a little sloppy, .., it feels correctly formed although the semantics or grammar have not changed substantially (although I could be wrong as I am thoroughly confused now).
So my questions are: are there any concise descriptions of how to use 'if' and 'if not'? Does this grammar usage have a name? When are they interchangeable and when not?