Quite a bit, actually. I’m a professional trainer, which means a lot of things. A few examples are: 1) Dog training is my livelihood, it’s how I make a living. Pet store trainers are store employees and, with few exceptions, work in the store stocking shelves, as cashiers, etc, when they are not holding a class. 2) Professional trainers usually have many years of experience training dogs using a variety of methods (because every single dog does not respond to the same approach). Pet store trainers can be hired with no dog experience at all, take a few-weeks-long course, and start holding classes. They usually are only allowed to use one method to train, and oftentimes only know that one method. 3) Professional trainers have worked hard to prove their knowledge and value by having at least one — usually more — national (and/or international!) certification. To earn these certifications, we’ve often have to prove our experience; have veterinarians, clients, and fellow dog trainers recommend us; be evaluated by other respected professional trainers; and in most cases, pass a national test. Pet store trainers’ accreditation is from the store they work for. A few do indeed have respected national certifications — very many do not.
I’ve heard people compare pet store trainers and professional trainers to getting your hair cut at a low-priced place like Super Cuts or going to a quality salon. The outcome — the quality of cut — is going to be vastly different in most cases. “You get what you pay for” generally applies here.