Owned by, yes. (Well, technically both are owned by the Avis Budget Group, rather than one being owned by the other.)

But is there any degree of linking between the programs???

It would be nice if anyone who is Avis Preferred was automatically also Budget FastBreak or vice versa, given that Avis and Budget are co-owned.

Otherwise, what's the advantage of their co-ownership to us (the customers)???