Shape and construction.
A surf style wakesurfer is as it sounds, built like a surfboard. This means they are shaped from foam with a wooden stringer through the middle for strength. Typically a surf style board is more high performance for surfing but they are considerably less durable as they are foam and fiberglass.
A skimmer style board is usually injection moulded and made from plastic so they can take some serious abuse. They are really easy to learn on so make perfect first wakesurf boards.