As a UX professional, I’m not convinced there really is a difference.
The article jonshariat links to makes a case for categories being mutually exclusive. If universally true, then that’s perhaps the one difference, but given that many sites use tags as a form of category browser, I don’t think that holds true either.
But let’s assume it does. From an end-user navigation POV, the difference is then whether or not your ‘buckets’ are meant to be mutually exclusive of not. So, perhaps that’s the question you need to ask…for the particular needs of your users of your site, should the data be put into mutually exclusive buckets, shared across buckets, or both?
As for ‘understanding’ that, well, that’s up to how you design the UI to navigate the structure.