From my experience, exclusive means that you sell it to one person only, and you are therefore paid a large(r) sum. Whether you loose the copyright to it is a matter of how the sale is setup.
Non-exclusive means that you can sell it to others too, you won't get as much money for each sale, but you can have many sales. This is mostly used for people who are just recording demos. They are usually not allowed to use it on a commercial CD, if so, they have to buy the exclusive rights to the beat.