Yes, they are both from the same car, front left and front right. It seems that a small plastic (nylon?) part has popped out, probably when releasing the belt, and disappeared. This part has the function of pushing the "lock" to the side so you easily can push down the "hook" and lock the belt. It is still possible to lock the belt, but I have to press the release button and wobble the part on the safety belt which takes some time.
And you are right, I would never dream of driving whithout the safety belt properly attached.
So I wonder if this plastic part could be replaced, or if it's necessary to replace the entire buckle.