No, there's no difference in air pressure between the two locations unless you own a hermetically sealed house. That's all the barometer is measuring.
You can test this with your phone if you get an app that reports its sensor values - most new phones include a barometric reading.
Oh, so that's what a barometer does!. It's strange but I have never bothered to figure out
how barometers worked, even though I have seen barometers hanging on walls since I was a kid.
Instead I just looked out of the window or listened to the weather forecast on TV. Much more interesting than a barometer hanging on the wall.
I just saw that big dial on the front of barometers saying Stormy, Rain, Fair, and Dry - and I just left it at that. No need to investigate further.
I never even bothered to ask why my various uncles always seemed to be constantly tapping their barometers. I
still don't know why they did that. Some kind of neurotic tic I suppose.
So, it's actually air pressure barometer measure! Very interesting-ish. For some reason I have always associated people with barometers as being a bit weird and compulsive, just like most of my uncles.
Fortunately for the world, the interest in barometers seems to be waning dramatically. I saw several at an auction last week and they only fetched 30 quid each...and they were obviously of very fine craftsmanship. Must have been really expensive when bought new.
I guess I'm not the only one who prefers to get their weather from the TV too.