So I have a cockatrice with a green heritage star and a cockatrice with a bronze-ish star. I have a good feeling that it has to do with deviant colors but why are the stars differently colored?

Those stars have nothing to do with deviants. Deviant colors are marked by an asterisk next to the color and yellow stars next to the deviant genes once they've been researched. Anyway cockatrice deviants haven't been released yet.

Green stars signify genetic power, which is gained by breeding level 50 and/or GP pets. Each GP level gives a 10 point bonus to the main stats.

Red stars signify degeneration which occurs when breeding pets that are related within 3 generations. Degenerate pets have a higher rate of bad mutations and bad genes have a higher power making them more likely to be dominant.

For more information check out the genetics and breeding section of the FAQ.