That is the idea. It is called dual control. On the old Chubbs, one key is a solid key stem (called a pin blank). The other is hollow (called a pipe blank). That way you will never put the key in the wrong hole.
If it is an original dual control there should be a hardened plate over each lock. Sometimes when it has been added as an afterthought there is no plate over the second lock.
You have, indeed, done well to get keys to the drawers. Those are often lost at some stage over the long life of such a unit.