Gage pressure ("psig") is pressure measured relative to ambient atmospheric pressure (approximately 14.7 psi).  That is, a gage pressure measurement does not include atmospheric pressure itself.

For a gage pressure transducer, one side of the pressure-sensing diaphragm must be vented to the local environment.  The transducer will then indicate a pressure of "zero" when it is not connected to the process pressure of interest, but while the sensing element is still exposed to atmospheric pressure.

Gage pressure is actually a kind of differential pressure.  It always equals the difference between the local absolute pressure and the local atmospheric pressure.

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For an absolute pressure transducer, the reference side of the pressure-sensing diaphragm is isolated from the local environment, being hermetically sealed in a vacuum.  (Absolute pressure sensors are thus not only isolated from environmental contaminants, but—theoretically—have better thermal performance than sealed gage units, because there is no trapped volume of gas to expand and contract with ambient temperature changes.)

The transducer will then indicate a pressure of 14.696 pounds per square inch at sea level, when it is not connected to the process pressure of interest, but with the sensing element exposed to atmospheric pressure.

Absolute pressure is always the sum of the local "gage" pressure (induced by some source) and the atmospheric pressure at the location of the measurement. 
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Differential pressure ("psid") is pressure measured relative to a specific reference pressure.  If the reference pressure is one atmosphere, the differential pressure equals the gage pressure.

Differential pressure may be either absolute or gage, as long as pressure is being measured in the same units at both ports.

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