(Pardon the deviation into my area of specialty)
@ghazzu is correct. In Florida, for instance, it doesn’t require $ to change hands, but that is often the way it can be proven, if a complaint was filed. In Florida, it includes “the determination of the health, fitness, or soundness of any animal.”
Therefore, having your trainer watch your horse trot up could be the illegal practice of veterinary medicine. Fortunately, there is a good bit of common sense used in evaluating claims of the unlicensed practice. But, it doesn’t require a complaint by an owner to have a case opened in Florida. If the Department sees unlicensed activity (ULA) a case can be originated.
There is, though, a total exemption for things any owner does to their own horse. Except for the treatment or vaccination of four things (rabies, brucellosis, TB, and EEE) any owner can do anything to their own horses. Except you could run afoul of animal cruelty laws on the County level, but other than those four things, it isn’t the practice of veterinary medicine if you own the animal.
But to additionally qualify, a trainer should not be “diagnosing” (or not) on a horse that belongs to a client. The Department, who prosecutes on behalf of the Vet Board, might not know about those incidents, but should a client decide to complain if there was an adverse impact, it can cause a huge problem. In Florida, ULA is criminal as well as prosecutable by the Department.