There is no difference. There are lots of species of Betta... Betta imbellis, betta rutilans and betta splendens just to name a few.
The normal brightly coloured shop bought species are betta splendens. Often all other types of betta aren't as bright as they come in 'natural' wild colours, and they aren't regularly stocked in many places.
A male may happily share his space with other fish, and a catfish that lives on the bottom and therefore not in the same territory as the betta stands a good chance, but some males just wont tolerate anything else living in the same tank.