For one thing, "fabric" is broader. It is not an absolute, but "cloth" usually means fabric intended for garments or clothing. You would probably say "fabric," not "cloth" if you were upholstering a chair, or decorating a wall, or covering the wings of a World War I airplane.

As uncountable nouns, they are very close in meaning. You could say that you bought 'some cloth' to make a shirt, although 'some fabric' or simply 'some material' would be more common. In this meaning, 'cloth' sounds a little old-fashioned. 'Cloth' can also be countable and have the meaning of 'a piece of fabric' . For example, 'Can you pass me a cloth? I need to wipe the window.'