AR has the goal of liberating animals from human exploitation, or to put it differently, to end *all* human activities that unnecessarily exploit or hurt animals (meat, fur, circuses, etc).
PeTA's simple founding principle is that "animals are not ours to eat, wear, experiment on, or use for entertainment". They have the right to live and live their own lives just as humans. It is wrong to think that they are here for us, that we own them, that we have the right to enslave them for our pleasure, just because we have more brain cells than them. We share the planet with all other living beings and we should recognize that. We *should* take what we need to live well, but exploitating sentient beings is clearly not something that is necessary to do so.
AW is not necessarily against the exploitation, slaughter etc. of animals for our pleasure, its goal is rather the "humane" treatment of animals in the process (whatever that means). You can be an omni and pro AW.
AR and AW are somewhat overlapping, and can have similar short term goals and strategies, but they are quite distinct concepts. A common misconception is that AW is a subset of AR, which it is NOT.