Is it an exit, or is it not?

There are some doors here at the hospital that confuse me...

It is obviously a door, but the sign on it says, "NO EXIT".

Here's another one... at the bottom of the stairwell that I use to go down to the cafeteria.

The meaning, I think, is that these doors are not to be used to exit the building in the case of an emergency. The first one (glass) goes into an interior courtyard. The second (wooden) goes into an interior hallway on the first floor. Just before it in the short hallway from the stairs to this door is a glass door leading into an exterior courtyard, which has no marking on the door, and a red exit sign above it. But, when I see a sign that says "No Exit", I interpret it as "Don't go through this door." Of course, if that was the meaning, why have a door there?

Side note: it used to be in some IBM buildings, there were signs on some doors that indicated, "This door should always remain closed" (usually between a stairwell and office space). One of my colleagues, Warren, raised the question: "If the door should always remain closed, why did they put a door there? Why not just make it a wall?"

And another question: Twice since we've been in the hospital (once each stay) there has been a fire alarm set off. The first time I looked out into the hall and the nurse or tech that I saw said that it was probably a drill and the doors to the rooms all needed to be closed. I was considering that there was a big chair with wheels on it in the room and that I could at least wheel Dwayne to the stairwell, though I wasn't sure what I was going to do after I got him there...

The alarm last night happened at about 2:30am. It happened that Dwayne and I were already up because he needed to go to the bathroom... in fact, I thought maybe he had accidentally pulled the cord in the bathroom because the first I noticed was the light flashing and alarm sounding in the bathroom. Again the nurse told me that it was a drill. Can you imagine what that did to the sleeping of the patients? It seems a bad time for a drill....

When I've been in a building and it has had a fire drill, I always thought that the procedure was to treat it as an actual fire and exit the building. If there were an actual fire, how would we know? Would the proper procedure be to close the door to the hallway and hope for the best? I hope we don't find out...