Much of the time (not all the time) when I meet people who describe themselves as an 'Artist', I find that they are the type that dabbles in lots of different media, but doesn't necessarily excel greatly in any of them. They have a 'creative spirit', but haven't focused on any one media or method enough to really hone their craft. Most artists I meet who do have a high level of craftsmanship describe themselves with more detail, such as 'painter', 'wood sculptor', 'portrait artist', 'fiber artist', etc. I think they have a great sense of pride in their craftsmanship.
Personally, I describe myself as a 'potter'. I make pots, so it's a simple, easy to understand description. I have had people say that it's not an adequate description, that I should say 'ceramic artist', but I feel no shame in making functional pots. I'll let my customers decide whether or not I'm an artist or just a craftsman. It doesn't really matter to me.