It is not intuitively apparent that we live in a world where every inch of our body is subjected to pressure (about 14.7 pounds per square inch at sea level). Evangelista Torricelli recognized this fact in the 17th century. He said, "We live submerged at the bottom of an ocean of the element air." The pressure exerted by the atmosphere in our gravitational field is also called barometric pressure, an absolute pressure that fluctuates with differing weather systems. The reason we don’t feel this tremendous amount of pressure is because there is an equal and opposite pressure exerted by the somewhat incompressible fluids of our body.
Pressure is a force applied perpendicular to the surface of an object per unit area. Mathematically it is P = F/A, where P is pressure, F is force, and A is area. Pressure is a scalar quantity, one that only has magnitude and no directional vector characteristics. In a practical sense we can think of it as a force that acts equally on all surfaces it is exposed to and results from the combined energy of the gas or liquid touching that surface. There are two basic pressure types - absolute and gauge - distinguished by what pressure they are compared to, which is called the reference pressure.
The standard terminology used to describe the physical characteristic in a pressurized system can be a little confusing to someone new to pressure measurement. Knowing the standard terminology provides a common language that will ensure what you want is what you get when purchasing a pressure gauge, pressure controller or calibrator and pressure transmitter, transducer or sensor. It will also eliminate a mismatch between the calibrated and the calibrator.
Gauge pressure’s reference is ambient atmospheric pressure. Absolute pressure’s reference is an absolute vacuum. So both, in a sense, are reading the difference between the reference pressure and the pressure applied. However, with gauge pressure, the reference pressure may vary depending on the current atmospheric pressure.
In situations where we have a vessel subjected to atmospheric pressure, we may want to ensure the vessel does not explode or implode. In this case, we can measure the difference between the atmospheric pressure and the internal pressure of the tank using a gauge pressure sensor with the reference exposed to the atmospheric pressure.
Differential pressure compares two arbitrary pressures. In essence, all pressure measurements are differential as they compare one pressure to another. Differential pressure usually is measured at elevated line pressures and is used to measure flow in a pipeline, level, density and even temperature.
Vacuum pressure, like gauge pressure, is referenced to atmospheric pressure but is a measure of pressure below atmospheric, and is expressed as a positive number.
Bidirectional pressure, also like gauge pressure, references atmospheric pressure but measures pressure above atmospheric as a positive pressure, and below atmospheric as a negative pressure.
This standard terminology makes a big difference when communicating exactly what is needed for a specific application.
For a visual explaination, check out Mensor's 'What are Pressure Modes?' video.