One might be inclined to think that they are one and the same, pretty much. Well, not quite.
We had this problem whereby the SSH worked fine but SFTP not at all. See the following desription:
SFTP seems to fail for NIS accounts under OpenSSH 5.x
Well, it ended up being a little different. What most of those NIS-based accounts had in common was a particular customisation in their BASH startup scripts (.bashrc, etc.) One .bashrc was removed the SFTP started working again.
Moral of the story? Whenever anything that could have to do with the login procedure goes wrong it might make sense to just maximally simplify the login procedure - such as remove all customisations, for instance - and try again.