How is a serf different from a slave?

The difference is that the serf is tied to the property meaning he was the lowest form of tenant of the land his rights if any were the rights vested in the land itself and slaves are tied to the owner meaning they are chattel - (discretionary disposable property) owned personally by the owner.

A lord of the manor could not sell his serfs as a Roman might sell his slaves. On the other hand, if he chose to dispose of a parcel of land, the serfs associated with that land stayed with it to serve their new lord; simply speaking, they were implicitly sold in mass and as a part of a lot.