Theoretically, no, but in reality, there is quite a large gap.
Let me start with some examples.
Some examples of albums that are generally considered art rock but almost never considered prog rock: The Velvet Underground and Nico, David Bowie's Low, Queen's A Night at the Opera, as well as later stuff such as Radiohead's Kid A, etc. Some examples of albums/bands that are definitely prog rock but not usually considered art rock: Genesis, Yes, Jethro Tull, etc. Of course, there are significant overlaps, e.g. Pink Floyd, King Crimson, etc.
So where does the line lie? Most people, I think, would agree that prog rock refers more or less to a rather specific sound, characterized by instrumental virtuosity, musical complexity, extended, multi-part compositions, and, more often than not, incorporation of classical/jazz influences. It's pioneered by mainly English bands in the late 60s and early 70s, such as Genesis, Yes, and Emerson, Lake and Palmer, but also American artists/bands like Frank Zappa and the Mothers of Invention, and continental European (particularly Italian) bands like Premiata Forneria Marconi. Anything that conforms to these lines is considered prog rock: Dream Theater, for example, doesn't really break any new ground in music, but due to their focus on virtuosity, complexity, and extended compositions, they're one of the prog rock/prog metal bands.
On the other hand, art rock is much more diverse. It's not really any specific sound: The Velvet Underground and Nico sounds nothing like In the Court of the Crimson King or The Dark Side of the Moon. But rather, it's about an attitude or an approach to rock, more or less. Art rockers try to break new grounds in terms of their sound, or try to incorporate "artistic" elements into their music, and they definitely try to think above and beyond "pop" music. Therefore, the results are very diverse, because they incorporate different influences and simply have different takes on their music. Sometimes, they overlap with prog rock, as with King Crimson, but often they could be the radical opposite of prog rock. The Velvet Underground and Nico is basically the opposite of what prog rock is, and much of so-called post-punk, while unabashedly opposed to prog rock, could definitely be given the art rock label. So, "art rock" is mostly an umbrella term that really describes a musical movement rather than a genre of music.
On a side note, a lot of prog rockers don't really try to break any new ground in terms of music. A lot of Emerson, Lake and Palmer, for example, is basically just rock but with rock cliches replaced with classical ones (or maybe vice versa), and same with Genesis and Yes, to a lesser extent. Not a whole lot of innovation here; but still they're undeniably prog rock! The label "progressive" often cause people to misinterpret and misunderstand the genre.
But, well, the lines can be really blurred sometimes. Business, geography, demographics, etc. also play a part in those labellings. Pink Floyd, for example, doesn't really display much virtuosity or musical complexity (more complex than your average rock band, but not comparable to most of prog rock), and while there are jazz influences on them, they make it quite subtle. David Gilmour actually went as far as saying that he was not a fan of "most of what you'd call prog rock"! However, Pink Floyd is almost universally accepted as a prog rock band. Most of krautrock really has little in common with British prog rock, but is nevertheless often classified with the British prog rock bands. On the other hand, the heavily krautrock-influenced Low by David Bowie is almost never considered prog rock proper. So, sometimes these labels are really arbitrary.
TL;DR Prog rock is mostly a specific genre of rock music originating mostly in the 1970s in the United Kingdom, while art rock is an artistic movement within rock music that emphasizes innovation, experimentation, and transcending the limits of "pop music".
