The structural difference is who you're acting for. An agent acts for someone else. They represent a client, owe that client duties, and get paid a commission out of a sale that belongs to their client. A wholesaler acts as a principal, meaning they're a party to the contract in their own name. They negotiated to buy the house themselves and then sold the right to buy it. Nobody hired them, and they owe no duty to the seller beyond the contract terms.
That's the reason licensing follows the pattern it does. Licensing law generally regulates acting on behalf of another for compensation, so a genuine principal falls outside it. Which is also why the whole thing is fragile: the moment you behave like an agent while calling yourself a principal, you've got a problem. If you never intended to buy, if you're shopping the house around before you have any contract, or if you advertise the property publicly as though you had authority to sell it, some states will look through the label.
Several have written that into statute. Illinois treats a second unlicensed deal within twelve months as brokerage. South Carolina restricts unlicensed wholesaling where the operator doesn't own the property. So the answer to "is it just what you call it" is that the name follows the structure, and if the structure is fake the name doesn't save you. Whether your particular arrangement counts as principal or agent in your state is a question for a local attorney.
One practical consequence: as a principal you have no duty to tell the seller what you think the house is worth. Many operators disclose their intent to assign anyway, in writing, because it removes the argument later.