I prefer the term tattooer, although any of them work. When I think of tattooing as a craft as opposed to an art, and myself a craftsman instead of an artist, I have an easier time setting aside my ego and giving the client what they want. There's nothing artistic about reproducing that same infinity symbol with birds and feathers coming out of it and hiding all of their baby's names and birth dates. The artist in me cringes every time. That's when the craftsman in me steps in and does it without complaining or putting ego in front of making a living. When I think of it as a craft that stress of having to create a work of art every time is lifted. The craftsman in me works a little harder on the little pork chop tattoos than the artist with the inflated ego who has to do it his way. That helps me sleep a lot better at night.
With all of that being said, all crafts are still art. There is art in everything you look at and I do mean everything. Somebody somewhere down the line designed the shape and appearance of almost everything you look at, from the box you pour your cereal out of to the toilet you take a shit in. Anyway, tattooer works for me.