If only we knew.
I'm a professional editor, so me pointing out others' word foibles is like Mike Tyson telling me I hit like a girl. Plus, nobody's perfect; I'm occasionally the reason the newspaper I work for has to run a correction. But you've got to admit it actually looks like somebody wasn't sure which way was correct and so tried it both ways, figuring one of them had to be right.
Neither one is.
The sign of the left says the only purpose of this door is for a facilities staff member to open it. (Presumably, the real purpose of the door is to protect something inside from falling into the hands of anyone who isn't on the facilities staff.) The one on the right says that the facilities staff can't do anything to the door except open it. (Can't even close it once it's been opened.)
What the sign-maker really wanted to say was "To be opened by facilities staff only" -- no one except facilities staff can open the door. (The facilities staff can do other things with the door: shut it, lock it; and the door serves other purposes than for the facilities staff to open it.)
That said, I can't imagine what would be so exciting behind either of those doors that anyone, facilities staff included, would want to open them. But then, only you live once. And you can only prevent forest fires.