I really don't know, but I just checked some Wikipedia definitions to make sure I am generally on the right track.
Felt is simply fibers that are compressed together, not woven. That is why, in general, felt cannot stand up to washing.
Fleece is a woven fabric. Polyester fleece is woven of fibers made out of polyester fibers that have a nap. Because it is woven, fleece can be washed.