A simple rule is that you cannot put any shrimp of the same genus together. Genus meaning the first word of the scientific name of the shrimp. Neocaridina heteropoda sp. "red" is the scientific name for the Red Cherry Shrimp. Red Cherry Shrimp is the common name. Scientific names are vital due to the fact that there can be many common names for the same shrimp, like Cherry Red Shrimp, Red Cherry Shrimp, Fire Red Shrimp, Cherry Shrimp, etc. For example: Neocaridina heteropoda is the scientific name for a wild type shrimp. Neocaridina is the genus, and heteropoda is the species. That is how you identify the genus, and then you can know what you cannot put together. You cannot house a Neocaridina with another Neocaridina. You also cannot house a Caridina with another Caridina. You can however house a Caridina with a Neocaridina.
Shrimp do not breed like other organisms where you can cross two species and combine the best characteristics. You cannot take a Snowball Shrimp and cross it with a Red Cherry Shrimp to create a "Pink Shrimp." Unfortunately selective breeding is the only way to create a colorful strain. Selective breeding is where you take the color traits of a wild shrimp and breed out the specific color you wish to have.