There are 3 red eye colors, pink, red and Ruby and they all dilute differently but all are considered red eye dilutes

A fawn, which the OP's newest ratty looks like is an agouti diluted from having ruby colored eyes.
A black rat with pink colored eyes is a champagne, a black rat with red colored eyes is a beige and a black rat with ruby eyes is called a Buff I guess, I'm not sure I've made any.