Concept art is used to conceptualize a larger work, like a movie or a video game and isn't generally meant to be seen by the public (Although sites like this are changing all that.)
Illustration is the retelling of a story in visual form, usually to support/help sell a text or other product, like a soda (Sundblom: Coca Cola) Illustrations are generally reproduced in conjunction with the product as a kind of label.
Fine Art is created by an artist for direct sale as itself, rather than a reproduction, usually with some gallery/market in mind. A fine artists works on "spec" or speculation, meaning as they are working they aren't sure whether what they are working on will sell.
There is no meaningful distinction between what actually appears in the art in any one of these forms. Although it is a general rule that Illustration and Concept Art are concrete images, rather than suggestive abstractions. Whereas "fine art" can be anything at all, from realistic pictures to dead sharks in formaldehyde.
I think some people get confused because these things can look the same, and socially, there are hierarchies in place that make this hard to come to terms with. The distinction is more clear when understand where these terms come from.
Concept artist is the Games industry equivalent to a Designer in Animation. In Games, Designer refers to the Game Designer.
Illustration comes from the Latin term, illustrio - "vivid representation", and was used to describe the quality of a text and/or graphics that accompanied it for visual enhancement.
Fine Art is technically an academic term referring to visual art that prioritizes aesthetics over utility. However it's generally understood as Art that isn't design.
If you consider a game/animation as the primary entity, then concept art, which serves to enhance that entity by visual development, is a form of illustration. However, when you detach an illustration from its intended context, it can also be Fine Art. So if you take some concept art out of the game studio, put a frame around it and hang it on a wall, it can be Fine Art. Vice Versa, if you take Fine Art out of the gallery and use it in a game, it can be concept art.
Thanks all, still a bit confused as to what catagory I'm supposed to be calling things in the attatchments editor etc. :op
Having recently just put up a gallery here, now I have enough decent pics to make one (by my current standards) It occured that I acctually didn't know what catagory to put them in. If anyone could take a look and let me know what they think I should be calling them I would appreciate it.