The most usual devices are barographs and barometers. A barometer can work off an aneroid cell (eg digital aneroid barometer) or a column of mercury (eg Kew Pattern barometer). Barographs usually work off aneroid cells and through a linkage system print the pressure onto a chart (usually changed weekly although there are daily barometers as well). So the main difference is that a barometer gives a spot reading while the barograph is continuous, although it's possible for the readings from a digital barometer like one connected to an Automatic Weather Station to be saved and called up later, or even printed out in graph form.
The usual unit for air pressure in meteorological circles is the hectoPascal (hPa) which replaced the millibar some years ago (the units have the same numerical value, though) except for the US which sticks with the old inches of mercury (InHg).