what is the difference between the two?

Typically, a ballast system is built into a boat, whereas a Fat Sac is a temporary ballast bag that is placed in a boat. Many ballast systems consist of Fat Sac-like bags that are plumbed into a pump system in the boat with switches on the dash. They do the same thing, but ballast systems look cleaner and are more convenient.

I think a custom ballast bag system with switches is much better than running hard tanks. Bags are less expensive, usually provide more weight, allow for more storage and easy access to the engine when empty.