Both “hydro” coming from Greek origins for water and “hygro” coming from the Greek “hygrós” for wet or moist, tend to be used in two terms for the same optical phenomena.
Hydrochromic or hygrochromic is a descriptor for optically active samples that change color with moisture content, most often inks, dyes and coatings.
Perhaps a distinction between these terms can best be thought of as related to the volume of water.
In extreme cases of hydrochromism, with the addition of water in quantity, the sample color can change from one color to another . In these cases color measurement can be used to verify lot-to-lot consistency in the extremes of the color shift.
In more subtle cases of hygrochromism with textile samples as an example, a change in relative humidity can cause a predictable change or bias in measured color values. In these more subtle cases, a conditioning cabinet can be used to standardize or condition the moisture content of the material.