>society has always tied both,

Pretty strong statement, an as such needs a non-tautological proof. Rich people buying rare things as what society should consider art may not exactly fit that bill.

The thing is what is considered art at any particular time is very nebulous and quite often tied to what the rulers of a country would allow. Trying to say that modern institutions get to decide what art is and isn't is also going to cause definition problems. Does folk art not recognized by museums count at art. The said people who like it would say it does.

Does a person who spends a small amount of time creating something that others consider art, even though that's not what they do, nor will they do it again, have they actually made a piece of art?

Simply put trying to put these rules on the ethereal concept of art quickly devolves into pedantry that makes actual enemies in fields were factions say their ideas are the only true art, and other factions that attempt to destroy the concept altogether.