More frequently spelled "Fine Art". I chose this spelling due to Fineart Forum an online magazine dedicated to the subject. Differentiated from the more general term 'art' in that it is created for it's own sake. i.e., not for profit, not for decorating some other entity (a publication, a building, a person, etc.) Art for art's sake as opposed to commercial art.
Some fineart movements include:
Those names not being considered Fine art would be Arts & Crafts Movement
, Advertising art
See the excellent debate that is Art does have an actual purpose.