Answer:
Animal rights is animal welfare PLUS the belief that animals have rights, which means they should not be killed or used in any way that does not include their consent.
A great example of animal "welfare" is Chipotle, or the ASPCA. PETA, ALF, and HSUS are all animal rights activists.
So similarly, animal rights derived from animal welfare, but other than that the two beliefs are NOT similar, at all. Animal right activists find animal welfare activists hypocritical. For example, a major difference is that animal welfare condones slaughter, experimentation, etc., so long as it's "humane".
However, due to the animal rights activists inflexible beliefs, diplomacy is hard to obtain, because they refuse to compromise an animal's well-being in anway. Many animal welfare activists believe that if they can achieve small steps helping animals, like more humane methods for slaughter, then it will eventually lead to mainstream animal rights ideology.