There's lot's of physical differences, but the only one that really matters is the size of the rear lug. If you fit the receiver for a Badger base with a smaller rear lug, then a DD Ross base won't be able to drop into the Badger receiver cuts. If you fit the receiver for a DD Ross base with a larger rear lug, then a Badger base will be loose when dropped into the DD Ross receiver cuts.
There's plenty of other differences as well: Machining marks/patterns on the top and side, chamfer vs round corners on the rear lug, sharp edges vs rounded edges in the base's areas above the receiver port and the cantilever front end, etc.