the purpose distinction is a pretty good one, but even that can get muddied - for instance... a lot of my favorite artists are considered "cartoonists" or "illustrators" rather than artists. their utility in their art is telling a story (cartoonists) or providing graphical context for something verbal (illustrators). but, you often see famous cartoonists like chris ware, seth, or art spiegelman having gallery shows in "fine art" galleries selling their original pages. so, does the original page, disconnected from the entire story, achieve fine art status once it is divorced from its context? or is it that the gallerist thinks that the art has sufficient name cachet that it can be sold as fine art, and with a fine art price? the latter case is where the accusations of snobbery come in - that the art scene has deemed that this or that cartoonist has risen above the low aspirations of his/her medium and thus deserves to have his/her work sold in a more rarefied realm, like the SOHO art gallery.
another way to look at it is that ALL art tells a story in some way. comics tell a story generally in a very linear manner (although there are always exceptions), whereas you have to dig a little bit more to find the more ambiguous story in a painting from a traditional fine artist, especially when you move into abstract or minimalist art. again, this is where snobbery creeps in - that any idiot can understand a cartoon book, but only someone who is sufficiently cultured can understand the story or meaning in a piece of string nailed to a white wall. in southern california, this dichotomy was what sprung lobrow art, since those artists were more interested in engaging their iconography (tiki heads, hot rod cars, hot ladies) than what was deemed artistic at the time. (another way snobbery comes in is when you look at art by someone like wayne thiebauld, who was famous for painting cakes and cupcakes, and although rejected at first, his art has become a key part of the american 20th century canon precisely because of its subversion of the idea that fine art has to have high subject matter. which is nice, although again with him it was a case of the art gentry conferring this lofty status on his art while still insisting on looking down their noses at other, lower forms of art.) at the same time, in new york, art spiegelman was curating the RAW anthologies, which showcased cartoonists in a setting that aspired more to fine art publications than newsprint floppies sold in candy stores (or porno arcades). the funny thing is, many of the artists in RAW, like jacques tardi or joost swarte, were already considered fine artists in Europe, where cartooning is given a seat at the fine art table, rather than relegated to the low culture ghetto it has been trying to break out of in the US for 30 years.
so yes, there is a clear difference between art designed to hang on a gallery wall and a park bench or flag pole, or even architectural flourishes like the famous art deco archways at paris metro station stops. but, with a lot of art, it gets muddy trying to categorize it as "fine" or as something else, which is why that determination is often left to those who are supposedly in the know.