The proper name for having two differently colored irises such as one green eye and one blue is heterochromia iridum, or more commonly heterochromia. In individuals with heterochromia the melanin pigmentation is not uniform in distribution and concentration.
Heterochromia is not always complete, you can have sectoral heterochromia. This is when just one part of the eye's iris is a different color I.e a brown eye with flecks of gray.
In hazel eyes the melanin distributed is always irregular. This eye is not truly brown or amber, or green or blue, It can have patches of those colors but it isn't one solid color.
Changes to the color of the body pigmentation is a characteristic of the genetic disorder Waardenberg syndrome. People with this condition often have unusual, large, wide set blue eyes or heterochromia with one blue and one brown. Heterochromia may be present not only in the eyes but hair or skin. There may be a patch of white in a dark head of hair or splotches of discolored skin in individuals with Waardenberg syndrome.
There are a lot of different subtypes of waardenberg, some are more extreme then others, many cases are benign, but medical conditions like deafness or spinal cord defects may be present in it's more severe forms.