It's easier for most people to simply lump these two together, and assume they are the same thing. Unfortunately, they are not, and more people need to realize this. The reason the Animal Rights movement has gotten so far is because the average Joe sees one of those HSUS advertisements about abused animals and says to himself "that's awful, I like animals, and don't like abuse. Maybe I'm one of those animal rights people!!" Average Joe doesn't realize that "those animal rights people" have just as much of an agenda as any other political group, and that they often don't want animals to be in anyone's lives.
See, the long and the short of it is, most "animal rights advocates" are actually "animal welfare advocates", but they just don't realize it.
Animal rights is about giving animals the same rights as humans. They want to go above and beyond the right to the needs of living, and go right to "animals can be more human than most humans!!" They are not merely people who love animals and don't want to see them abused, they are people who think that animals are better off without humans. They often express their opinion that an animal's life is worth more than a human, and that breaking the law is okay if it's "for the animals." These people don't care who they hurt, and would turn in their own mother if they thought she might be neglecting her goldfish.
To an animal rights advocates, there are no good breeders. None. All animals who are bred are abused and neglected(when owned by breeders), or their owners are irresponsible and lazy(when they are family pets who haven't been desexed). All breeding operations are puppy mills, all breeders evil. Breeders are absolutely only in it for the money, as far as they are concerned.
An animal, to them, is not a pet. It is a "fur baby" or a "rescue" or a "refugee", and only animal rights advocates are fit to have them. If anyone else has a pet, it is a slave, a captive. They feel that animals should have no contact with humans, that we should not have domestic cows, or use or eat any part of an animal. No milk, no eggs, no leather wool or fur. No meat. No animal testing or experimentation of any kind. No service animals - including bomb and drug dogs, land mine searching dogs, seeing eye dogs, police dogs, police horses, helper animals of any kind. No farm animals, no riding or driving horses. No working farm dogs, or guard dogs. No pets. No domestic animals should exist. Zoos and aquariums are prisons and should not be allowed to operate. Animals should be left in their natural state, and not interfered with at all.
The majority of animal rights advocates are vegans(and the rest are hypocrites), and they aren't afraid to let you know that they are, or why they are. They don't feel that animals should die to feed other animals, and will often put their dogs or cats on a vegan diet, despite it being very unhealthy for the animals. They tend to make a great big production about being vegan, and make it into as big an ordeal as someone with a severe allergy. To them, eating a veggie burger that was grilled on the same grill as a regular burger is a life threatening incident.
To sum it up, an animal rights activist feels that anyone who profits from animals(with the exception of executives at PETA, HSUS and other like-minded organizations) is absolutely evil. No one should eat, wear, own or use animals in any way, shape or form. I wouldn't be surprised to find out that animal rights activists even boycott photographers who take nature photos.
On the other hand, an animal welfare advocate is someone who loves animals and wants them treated well. They may or may not be vegetarian/vegan, but they don't generally try to force their eating habits on you. They will have pets, and they may call them annoying names such as "fur babies", however they don't think that anyone else's pets are slaves or captives.
Animal welfare advocates support ethical breeders, and ethical farming. They know that there is a vast difference between a huge factory farm and a small local farmer. They make this distinction, and they are aware that there is a place in this world for farmers and breeders as well as for rescues and vegetarians. They are more inclined to be willing to live in harmony with those who disagree with them.
Often, you are able to have reasonable conversations with animal welfare advocates, without them resorting to name calling or threats. They will be more willing to see both sides of the fence, even if they are comfortable where they are. They do not react as emotionally, nor as vindictively. They are the ones who comment things concerning the animal, wishing the animal well and speaking well of the person who took it in, rather than saying that whomever did that needs to be shot and peed on.
Animal welfare advocates can see the need for zoos, especially captive breeding programs for endangered species. They understand that not all of these places are bad, and again, can differentiate between them. They are not going to vilify people who may make a profit from animals, as long as those animals are well cared for.
Unfortunately, the problem with animal rights/welfare advocates and everyone who isn't an animal rights/welfare advocate is that no one can really agree on what is proper care. There will never be a group meeting where everyone can say "this is okay, and this is not." Take, for example, the Flat Creek Border Collies case. I thought those shelters were adequate, but the animal rights and animal welfare advocates did not.
Basically, animal welfare advocates are usually a little less on the crazy side than the animal rights advocates, but not on the same page as people who work with animals in any capacity other than rescue or pets. I prefer an animal welfare advocate over an animal rights advocate, but would really much rather have a discussion with someone who is like-minded or willing to consider other view points. Both animal rights and animal welfare advocates usually feel that their way is the only way, though some animal welfare people are more lenient towards different standards of care.
I hope that this will help clear up some confusion as to what people mean when they talk about animal rights and animal welfare. Of course, it is not a black and white question, but many shades of grey, leaving some people to tend towards the extremist side, and others to be far more lenient. Only you can decide if you are animal rights, or animal welfare, and I encourage everyone to do their own research and form their own opinions and positions.
I shall leave you with one of my favourite quotes of all times, a statement made by the owner of the Bomanville Zoo and the controversial elephant that lived there.
"I don't believe in animal rights. To have rights, you need to be able to take responsibility for your actions, and animals can't do that."