These smaller versions have a specific task. The barometer on the left shows air pressure and is just a smaller version. 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.