There's a lexical ambiguity between these words much of the time. Or, more specifically, whether seems to be used in a subset of cases where if would be used. And the prescriptive perspective is that if should not be used in the cases where whether can be used. So to some extent we seem to have a straightforward ambiguity between them (rather than a more complicated overlap):
I don't know whether that's the right answer.
vs.
I'll tell you if you give me $5!
However, I think I just came across a case (in my own writing, an email, actually) that blurs this distinction. It only works with "if", but it has a meaning that is closer to the "whether" meaning:
I'll tell you if I'm ever in town.
Technically this could have a reading where I'll tell you regardless, but in some cases that's not the intent, as with "ever" here. That doesn't really work with "whether":
I'll tell you whether I'm ever in town.
Awkward at best, and not the same meaning.
And it's not purely conditional either.
So is this an amalgam? Any thoughts?