Artwork basically means any art that someone has made. It can be an amateur who does it for a hobby, it can be for commercial purposes. We use work of art to describe something of high quality.

I would say "artwork" more heavily connotes a collection of art. Paintings, sculptures, photos, etc. "He showed the buyer some of his artwork to gauge her interest." "Work of art" refers to a single thing someone created. Painting, sculpture, etc. Also connotes it is quite good-looking, I would say. In fact, the phrase "work of art" is often used to say something like, "Wow, that thing is a work of art!" Meaning, approximately, "That thing is gorgeous / really well crafted / beautiful!"