The definition according to DIN 1314, February 1977 (extract):
2.1 The physical variable pressure p is the quotient of the normal force acting on a surface and the area A of this surface:

2.2 Various pressure variables are employed in engineering, and although the majority are differentials of two pressures, they are also referred to simply as pressure in normal engineering usage. As this can lead to misunderstandings, it is recommended to use the terms defined in sections 2.2.1 to 2.2.3.

2.2.1 Absolute pressure:
Absolute pressure p_abs is the pressure above the zero value of pressure in empty space.

2.2.2 Differential pressure:
The difference between two pressures p₁ and p₂ is called the pressure differential D p = p₁ – p₂ or, if it is a measured value itself, pressure differential
p_{1, 2}

2.2.3 Atmospheric differential pressure, gauge pressure:
The difference between an absolute pressure p_abs and the given (absolute) atmospheric pressure p_amb is the atmospheric differential pressure pe; it is called the gauge pressure: p_e = p_abs - p_amb
The gauge pressure p_e takes on positive values when the absolute pressure is greater than the atmospheric pressure; it takes on negative values when the absolute pressure is smaller than the atmospheric pressure. ...

3 Units (see DIN 1301)

3.1 The SI unit of pressure is the pascal (unit symbol: Pa):
1 Pa = 1 N/m²

3.2 One tenth of a megapascal (unit symbol: MPa) is a bar (unit symbol: bar). 1bar=0.1MPa=0.1N/mm²=10⁵Pa. …

Conversion of obsolete units of pressure into pascal and bar: The previously used units of pressure kilopond per square centimetre (kp/ cm²), technical atmosphere (at), physical atmosphere (atm), torr (torr), conventional metres head of water (mH₂O) and conventional millimetres head of mercury (mmHg) are converted into the SI unit pascal and the unit bar using the following equations:
1 kp/cm² = 1 at = 98 066.5
Pa = 0.980 665 bar
1 atm =101 325 Pa = 1.013 25 bar
1 torr = = 133.322
Pa =1.333 22mbar
1 mmHg= 133.322 Pa =1.333 22mbar

1 mH₂O= 9 806.65 Pa = 98.0665 mbar

The most important pressure for designing and operating a mechanical seal is the effective sealing pressure acting on the mechanical seal. The quoted pressures are usually gauge pressures. Nevertheless, it is advisable to give an unambiguous pressure specification, especially for pressures close to atmospheric pressure.