The nuclear reactor is different from the breeder reactor because it generates energy through fission. Historically, in order to be called a breeder, a reactor must be specifically designed to create more fissile material than it consumes. this is what I've looked up and been able to find
Neutron radiation turns fertile material into fissionable material. Often reactors are designed to be both fission reactors and breeder reactors at the same time, though this is not a true breeder reactor.