No it isn't a translation, but there are connections.
The crucial thing to realise is that "art" (and its equivalents in Greek and Latin) have had a broad range of meanings. The Oxford English Dictionary lists 12 primary meanings for the noun (some of them further subdivided). It starts off meaning "skill", and then comes to denote different fields in which one might apply skill.
But the modern distinction between "art" as in fine arts and "technology" would have been barely intelligible to the classical Greeks.
I think "state of the art" uses "art" in a somewhat old-fashioned way, to mean a field of endeavour and creation, not necessarily artistic in the way we usually understand that word today.