skttl969 has earned a best answer, IMO, but I'd like to add something to her excellent explanation.
Commissions and skullduggery in buying and selling horses can be a real issue. Most trainers are honest and ethical, but there are some who are not and that's where you as a buyer have to be aware.
If you are buying a horse and a trainer is acting as agent in the purchase, here are some questions you MUST get answers for:
Who actually owns the horse? If the trainer who is representing you in the purchase of the horse, or the trainer who is representing the seller, won't tell you who actually owns the horse, walk away from the deal. Ask the trainer representing you if they have an ownership interest in the horse, or if the seller's agent has an ownership interest in the horse.
Can I talk to the seller directly? I know some trainers don't like clients doing this and some sellers prefer not to be involved in the transaction, but this is one issue I would not be flexible on: I want to talk to the person who actually owns the horse, who will be getting my money if I am buying the horse. If I can't do that, no deal.
How many people in this transaction will be getting a commission on the sale of the horse? Trainers make part of their living collecting commissions on the sale of horses. If Trainer Tina asks Trainer Charlie if Charlie has a horse, and Trainer Charlie asks Trainer Robert, and Robert has a horse, it's likely that Trainer Charlie and Trainer Robert are getting commissions on the transaction, as well as Trainer Tina. Ask your trainer who is getting paid a commission on the transaction. (In an ethical world, Tina would split whatever commission she's getting from her client with Charlie and Robert. But it isn't an ethical world, and the 10% or so that Tina is getting from the client isn't very much when it has to be split 3 ways. In an unethical world, Tina will increase the price she charges the client for the horse to cover whatever Charlie and Robert are getting as commissions. Client pays.)
If a trainer is representing you in the purchase of a horse, and you are paying the trainer a commission on the transaction, by law in many states the trainer is required to disclose to you if they are receiving any remuneration from the seller on the transaction. When a single agent receives payment from both buyer and seller on a transaction, this is called dual agency. It isn't necessarily illegal for someone to represent both parties in a transaction, but it sure as hell is unethical for them to fail to disclose that, and in some states it is illegal to fail to disclose dual agency. But there are trainers out there who will pocket money from both the buyer and the seller and will just keep quiet about it, figuring that what the client doesn't know won't hurt her. Dual agency is a situation that is absolutely ripe for conflict of interest.
Last warning: if you are buying a horse and the trainer representing you in the transaction tells you, when you go to close the deal, to make the check out to anyone other than the person who owns the horse you are buying, be very, very cautious in proceeding. I would go so far as to say that you should walk away from the transaction. My preference is to hand the check directly to the seller and receive the bill of sale directly from them. Make sure that the bill of sale you receives specifies the price you paid for the horse. (If the bill of sale is handed to me by anyone other than the owner of the horse, my preference would be to call the owner and make sure that the amount I paid for the horse is the amount they sold the horse for.)
I hate to sound so suspicious, but it's my experience that there are trainers out there who regard trusting clients as little woolly lambs, ripe for fleecing, and who will not behave ethically. Protect yourself in a transaction and make sure you and any trainer who is acting as your agent are very, very clear about who is receiving a commission, how much that commission is, and who the commission is coming from. If you have the slightest suspicion that someone acting as an agent is not being complete transparent and honest about the transaction, keep your hand on your checkbook and your eyes wide open, and walk away.