They're all mixes bred to lay well. They're not mixes of the same chickens though
You can do some searching, many of the hatcheries will tell you what they breed to get a particular sexlink. Going off the top of my head, black sexlinks are RIRxbarred rocks, perhaps? Red sexlinks vary a lot, could be RIR over leghorn, RIR over white rocks, RIR over RIW (which I think are Isa's), or RIR over delewares.
Isa-browns are a cross between the best RIR and RIW, they make a hybrid that lays over 300 eggs in the first year. Red sex-links are the worst breed. they are the loudest chicken, they are usually bred for the maximum egg production. I would suggest get isa-Browns if you were to choose, black sex-links are crossed by RIRxBR they are not the best layers either, they might lay 5 eggs one week and go a couple of weeks w/o laying eggs. same way with red-sex links.
Love my Gold Sex-links. They lay huge eggs for me very consistently(pretty much daily) - nearly 3oz. per egg!!! But I don't know if it is just my girls, or if that holds true across the board. Got more chicks this year, and they are very sweet and docile - as are my girls I got last year.