Generally speaking, I slot art into 4 categories: cartoon-cartoon, cartoon-real, real-cartoon and real-real. (Incidently, I got the idea from an essay Dave Sim, creator of the comic "Cerebus", wrote pertaining to various styles he implements in his art. His terms are like mine, though he replaces "cartoon" with "fantasy").
Real-real is photo-realistic art. This style is the ideal aspired to in most Renaissance paintings (da Vinci!), in portraits, some illustrative work (esp. fantasy art, of all ironies!) and even in some comics (rare, as photo-realistic detail is time-consuming, but you can look to "Arkham Asylum" - published by DC comics - for an excellent example of real-real comics).
I'd even slot Dali and Giger into the real-real category, even though their surrealist illustrations can't exist in this reality, the style - in terms of perspective, texture, detail, etc. - is still photo-realistic. In other words, if a watch could melt and drip over a tree, that's how it would look when it did so. These descriptives are all in terms of style, not content.
Real-cartoon drops some of the photo-realistic detail in favor of some exageration of either important features or expressions. The comic book industry often makes use of real-cartoon artists (ie, Frank Miller), though they are by no means the only artists allowed to compete in that medium. A number of animated movies are real-cartoon, such as Ghost in the Shell, Akira and Heavy Metal, as well as some animated TV series; Transformers, G.I. Joe, Gargoyles and the new Jonny Quest. It can be a very close call sometimes between real-cartoon and...
Cartoon-real. More photo-detail is dropped, characteristics become more exaggerated and the whole "look" of a piece becomes more stylised. Disney's The Little Mermaid, Beauty and the Beast and The Lion King were predominantly cartoon-real (with some instances of cartoon-cartoon... although, the backgrounds grew dangerously close to real-real in some instances), as is the animated version of The Hobbit and Lord of the Rings. Many comic book artists go for a cartoon-real look, such as Todd McFarlane, Erik Larsen and Dale Keown... mind you, their detail isn't lacking at all, but the exaggeration of gesture, emotion and physique takes them too far away from realism for me to call them real-cartoon. Much Japanese cartooning (anime and manga) falls into this category as well (Sailor Moon, Ranma 1/2, Robotech, etc.), though anime and manga are perfectly capable of running the gamut from real-cartoon to cartoon-cartoon (and in some exceptional cases, the props & backgrounds of the real-cartoon works will be real-real!)
Cartoon-cartoon is pretty clear; this is the playground of Warner Bros., Disney and Hanna-Barbara as well as the typical style of newspaper cartoonists. This is what most people think of when they think of cartooning. I think we see enough cartoon-cartoon stuff that I don't have go on with endless examples and nit-pick fine detail. Realism is almost completely replaced by iconography, exaggeration rules the game and anything goes.