Facebook generates a Post record when I rename a group's name or just an ActivityItem?
While I can't comment how Facebook works internally, in terms of relational design, a normalized schema would have these two actions in separate tables.

This would be done because the other bits of information associated with each action would be very different.

Changing a group's name would probably involve inserting a history record with the old name, and updating the current record with the new name. Notifications could have other things associated, such as comments and likes.