1. PSI/Pa: These are imperial/metric units expressed as a force per area (yes, all pressure is a force per area, in this case though the definition is a 1:1 between a force unit and an area unit). These are commonly used in engineering as you will frequently have two of: Force, Area and Pressure/Stress and when you need to find the target value it’s a simple multiplication/division calculation. There’s also things like pounds per square foot, kips per square inch, kPa and so on depending on use case.
2. Bar: This is 100,000Pa, it’s also fairly close to air pressure at sea level – generally off by about 1-2% depending on weather. Sometimes more in severe weather. Has similar use as PSI/Pa, but commonly applied for things being pressurized by gasses.
3. ATM: This is a weird one. It’s a measurement of air pressure at a very specific temperature and altitude, but has an awkward conversion to force – 1 ATM equals 101325 Pa, or just over 1 Bar. It’s kinda a relic, I’m not sure of any formal use for it as any conversion to force requires scaling the value after multiplying by area.
4. Mercury: One of the instruments used to measure pressure is a U shaped tube with mercury in it. One side of the U can be pressurized to a different pressure than the other – forcing the mercury to one side of the U. By measuring the height difference you can measure the pressure. This unit is useful when all you care about is knowing the pressure and you don’t need to convert to a force, so you can just read the length off the device using a readily available ruler – the most common use the average person will see for this is the blood pressure measurement device used in medicine. Similar devices exist using water, but result in much larger measurements because water is so much less dense – a blood pressure measurement tool using water would need to be something like 8-10 feet tall, so somewhat unwieldy.
Latest Answers