A mutation would be like the difference between a black labrador vs a yellow labrador... or a normal orange bengal tiger vs a white bengal tiger. You can breed two different mutations together from the same species (or, in the case of dogs, breeds) and you will always get the same animal in the offspring. Depending on the genetics will depend on how the offspring turn out. In tigers, the white mutation is recessive, so if you were to breed a white bengal to a normal wild type/orange bengal, all the offspring will be orange split white. However, if you breed a white bengal to an orange split white bengal, you'll get a combination of orange and white offspring. White bengal x white bengal you get white offspring. Orange split white x orange split white would also result in orange and white offspring.
A breed would be more akin to the difference between any dog breed (labrador, pug, greyhound, great dane, etc) as compared to a grey wolf. Dogs have been domesticated enough, with enough variants that we can no longer call them a wolf. It's not just dogs, as you have cats, pigs, cattle, etc. Basically, any domestic breed of animal that could no longer be considered anything similar to their wild counterpart. If you were to breed two different breeds together, you would get an animal that is somewhere in between the parent breeds. That is, the animal will have characteristics from both parents. A labrador x great dane will create a dog that is smaller and more slender than a great dane, but larger and bigger boned than a lab. Legs may be lengthier as well when compared to a lab. A lot of corgi mixes on the other hand may end up with the short legs of the corgi, but if bred to a larger dog breed, will have characteristics of the larger breed in head shape and overall color. They may be larger and taller than a typical corgi, but will be terribly short as compared to the larger breed.
It might be possible to say that Neocaridina davidi that we have in captivity are now a breed, but all the different colors would be considered mutations. If you mix colors, there's no guarantee that the resulting offspring will be a combination of both parents. Most often, the offspring will be one color of one parent, or they'll be wild type. If you breed two similar colors together, then it might be possible to get offspring that are similar to the parents. Breeding bloody mary to any cherry color for example will just result in red offspring. Breeding Blue Dream with Blue Diamond will result in more blue offspring that may have black markings. Breeding Yellows with Greens and you could have a mix of yellow and green offspring. (some yellow colonies can throw green offspring) However, breeding cherry with yellow and you could get wild type. Or maybe it's green jayde to blue dream and the offspring are wild type. Without knowing the genetics or doing test breedings, we don't know if the mutations are dominant, co-dominant, recessive, sex-linked or?