You're selling your position in a contract, not the house. When you sign a purchase agreement with a seller, you now hold the right to buy that property at that price. That right is a thing you can transfer to someone else for a fee. The document that does it is called an assignment of contract, and the fee is the assignment fee. The seller still sells the house, your buyer still buys it, and you step out at closing with your fee.
That's the strict meaning. Loosely, people say "I'm selling a deal" or "selling a contract," and they mean the same thing. Nobody in the room will correct you for saying it the loose way.
On the license part, your supply house guy is half right and the half he's missing matters. Public advertising is one trigger that some states treat as brokering property you don't own. It isn't the only one. Whether your activity needs a license depends on your state's real estate statute and how its regulator reads it, and that genuinely varies, so ask a real estate attorney in your state before you sign anything. What reverse wholesaling does is remove the marketing question. It doesn't answer the licensing question for you.
The part that catches new people: your purchase agreement has to actually permit assignment. If the contract says non-assignable, or the seller is a bank or a HUD listing, you can't hand it off no matter how good your buyer is. Read the assignment clause before you get excited about a match.
