What is the difference between a fief and manor?

The answer depends somewhat on how specific or particular you want to be. A fief is the land granted to a vassal under feudalism. A manor is an isolated, self-contained village of sorts that is the entire (or less) land of a fief. A manor is typically 1000 acres and approximately 200 people. It is built around a manor house. Technically, there could be many manors on a single fief. So while a fief is the land granted by a lord to a vassal, the manor is the specific economic system of the manor-centric living system of the peasants and nobles in the middle ages.