More info in the Introduction of Jeppesen charts if you have them handy.
But in a nutshell:
HAT = Height Above Threshold
DA = Decision Altitude
DA is associated with precisions approaches (electronic glideslope).
DA is the altitude above mean sea level at which the pilot must have certain visual cues (e.g. lights) in sight in order to continue lower towards touchdown.
DH (= Decision Height) is the difference between DA (in MSL) and the elevation of the particular runway threshold.
MDA = Minimum Descent Altitude and is associated with non-precision approaches (no electronic glideslope).
HAT is the difference between MDA and the elevation of the particular runway threshold when landing "straight in" (more or less).
If circling then HAA = Height Above Airport and is the difference between MDA and airport elevation because you could conceivably circle to land any runway (unless stipulated as circling prohibited).
FYI = For Your Information.
Professional pilots continually confuse the terms DA, DH and MDA.
Your attention to detail will separate you from the rest.
