I think they're just different colour

Wildtype lovebirds are mostly green with a variety of colours on their upper body, depending on the species. The Fischer's lovebird, black-cheeked lovebird, and the masked lovebird have a prominent white ring around their eyes. Many colour mutant varieties have been produced by selective breeding of the species that are popular in aviculture.

But many species can interbreed with various levels of viable offspring.