There are various viewpoints as to what qualifications allow a person to title themselves a behaviourist as opposed to a trainer. Some people feel only veterinarians can be behaviourists. I feel these are two very different professions, and although a person could be both, the ability to excel at both at the same time would be tricky. Some people believe a behaviourist requires a degree. I can see the validation in that, and in particular a degree in psychology; however, the ability to learn psychology can be achieved outside the classroom. The ability to learn from dogs can only be achieved by working with dogs.
I feel the differences lay mainly in the rehabilitation techniques, mainly "Reactive vs ProActive" techniques. For example, if the issue is messing in the home, than a trainer is better suited for house training a puppy, where the techniques of responding negatively to messing in the home vs a positive response when going outside (for example) is effective. A behaviourist is better suited if the messing is due to anxiety, or the dog did not learn to be house trained during puppyhood and the standard techniques are not working successfully. As a behaviourist, I do not teach "right vs wrong" in the same way a trainer would. For example, if a puppy is stealing socks, than a trainer would apply Replacement techniques (remove sock, give toy), Many dogs know the object is wrong to take (which is why they are doing it), so. as a behaviourist, I teach my clients how to calmly work with their dog so that their dog does not want to take the sock. This is requires ProActive, not Reactive techniques.