ghost is someone who has passed on and is "stuck" between the physical world and the Afterlife. They do not cross through The Light to go on to the Afterlife, but stick around in this "netherworld" for one reason or another.

A spirit is a person who has passed on, but has actually gone through The Light and into the Afterlife. There they go through a life review learning process, and after that, are able to come and go between the Afterlife and our physical world. 

Spirits come back to watch over us, and to comfort us. Ghosts do not. I hope this helps, but if anyone has any more questions, I'll do my best to answer them.