Craft, as an activity separate from art, aims to produce useful objects, which are more or less fit for purpose and more or less beautiful. Art aims to produce objects solely for aesthetic appreciation (which are therefore more difficult to judge).
Craft, as a
part of art, is the application of traditional skills that the artist has been trained in. Or more loosely, it is the skill or technique involved in making a work of art. How important is it? I'd say very important, but it's more complicated than a linear scale of skillfulness.
They say that Van Gogh was not as accomplished a painter as Picasso, but I don't think we can say that he was an inferior artist. I suppose we
might say that because Picasso had mastered the traditional artistic skills, he was more able to revolutionize art in the way he did. Things seemed to come easy for him; was that because of technical mastery?
Similarly, there have been many more technically able guitarists than Frank Zappa or Robert Fripp, but the music of, say, Yngwie Malmsteen and Steve Vai leaves me cold. Could this be because Zappa and Fripp had other skills, not particularly involved in guitar technique, that they brought to bear on their guitar playing (harmonic awareness, note choices, etc., that they got from being composers and having a natural all-round musical knowledge and musicality)? Or do we in this case want to reach for the arty stuff to explain it: conceptual vision, emotional investment, or imagination?
Some painters are terrible at painting hands but great at other things. Can we only say they are great once they've finally managed to master hands?
It becomes apparent that craft, skill, and technique are not the same thing, or can at least encompass a range of different and overlapping kinds of abilities. One answer is that craft (and possibly technique) is the set of traditional techniques that are handed down by training, whereas skill seems to be something wider or more general.
I wouldn't want to say that art = [craft, skill, and technique] + [vision, emotional investment, imagination], because it seems simplistic and reductive, but it might be a way of looking at it. For instance, some conceptual artists have the second addend, and the first is applied by the employees of the artist. And what does this say about conceptual art?