This makes perfect sense to me, and bumping into the wall will let you know the difference.

A different message would be preferred.

Actually, overall I'd say the secret door message should be more explicit for new players - like "You hear a hollow thud" or "You hear a creaking sound". The kicking method to find doors is pretty frustrating when trying to look out for a slightly different message, and it's silly that you have to be spoiled to really understand it.

I don't see why you would feel the same way by bumping into a secret door and into a undiggable wall

Well, you really hurt your foot both times. That makes sense, to me, but I wouldn't object to another message for secret doors.

I agree to this. It also would be nice to add a small chance that the wall might fall on you, although this might be abusable as a way of digging...

Yes, I think that message about "really hurting", which is also not true, as damage is the same (and it shouldn't be another) and most of the time it's 0, is totally illogical and unintuitive.
Message about some sounds you hear would be a lot better.