The difference is just perception. Sheet lighting is basically fork lightning that is obscured by the clouds or distance and appears to be a diffuse light rather than a well defined light, such as a lighting bolt or forked lightning.
Forked lightning is a very violent and sudden discharge of electricity, usually between a cloud and the earth. It may be compared to the spark discharge between the poles of a charged Leyden jar. Sheet lightning is a silent discharge over the surface of a cloud. Very little is as yet known about its nature. It should be pointed out that what is often referred to as sheet lightning is merely the lighting up of the sky by flashes occurring out of sight beyond the horizon.