David,
1. usually both terms are applied to the same thing.
2.
Literally they are different.
"Игровой" means - and thus emphasizes - the play of the actors (as opposed to animation, or historical footage).
"Художественный" means and emphasizes that it is an art. Mostly it is used in the sense "as opposed to documentaries", the same way as 'fiction' is applyed to books as opposed to 'non-fiction'.
Animated films are rarely called this way, so we have #1: 'applied to the same kind of things'
But we understand that both documentries and cartoons are "art" as well.... so the term used this way sounds non-strict somehow.
3. In TV channels listings you meet numerous 'худ. фильм" and 'документальный фильм'.
This is what makes designation "художественный фильм" familiar to us.
Colloquially you just say 'фильм'! Without a context, people think about 'live-action', 'fiction'.
Or you say "мультфильм", "документальный фильм" etc. when it is an _ordinary_ cartoon or documentary (sometimes you might want to avoid these words because they bring misleading images and say just фильм).
You would use terms "игровой" or "художественный" when there is some _confusion_. E.g.:
– Это мультфильм?
– Нет, на этот раз это игровой фильм, основанный на аниме.
– Это документальный фильм?
– Нет, художественный.