Other than standard grey, there are only six common colors: white, sapphire, violet, beige, black (velvet), and ebony. Both MCBA and ECBC classify chins by these six colors, as well as a section for standards.
Hybrids are combinations of those six colors, such as pink white (white + beige), tan (beige + ebony), TOV white ebony (black + white + ebony). You can take the above listed six colors and put them in any combination and have a new hybrid. The more mutations in one animal, however, the less likely you are to get a show quality animal. Both organizations classify hybrids into one of the six color sections - anything that is white will go into the white section no matter what other colors the animal expresses, for example. Tans and brown velvets go in the beige section, TOV violets would be in the violet section, etc.
Of those six colors, sapphire is the least common but it is not "rare." There are rare colors, such as Goldbar, Lowe Recessive White, and German Violet, and maybe more that I'm unaware of. These colors are not "recognized" at shows - even though they are completely separate genetic mutations from the common six, they would still be classed as one of the six if shown, such as the Lowe Recessive White that was classed with the other whites. More often than not, though, they're not brought to shows as very few breeders have them and those that do are dedicated to improving them to the point that they can compete against the other common colors.
As for ****/hetero, as Stack said, it refers to the genotype. A **** beige has two copies of the beige gene and because of that can only produce beige and beige hybrid kits. A hetero beige has one beige gene, the other gene is not mutated. A hetero beige can produce beige kits if they inherit the beige gene, and standard kits if they inherit the non-mutated gene (genes inherited from the other parent notwithstanding).
