The barometer on the right has a more specific job, showing height. This barometer is known as an altimeter. Hikers in mountainous regions use this to see how high they are. Altimeters can be so sensitive they can even detect the height of buildings. One drawback is altimeters depend on air pressure for their base, should the pressure change then the reading will be inacurate.
Airplanes use altimeters to estimate their height as well.
You've seen these barometers, known as a banjo barometer. These are the same as any other decorative barometer but it does have its origins back to the 1800's. The reason for the long stem is to make it look more like a Fortin's Barometer. Its a marketing ploy. The large mercury barometers were cumbersome but also fashionable 100 years ago when aneroid barometers were plentiful builders wanted them to LOOK like a the more expensive Fortin's.