how exactly is a franchise different than a dealer?
Good question.
A dealer is just someone who makes a deal with a manufacturer of a product such as a car, to sell the manufacturer's product(s) exclusively at retail, but this "dealer" uses his own name, example, "XYX Chevrolet", and apart from commiting to a possible annual sales quota, and agreeing to provide certain standard services, such as warranty and other repairs, the dealer has complete freedom to choose his own location, design the look and layout of his dealership, set his own prices, and handle his own advertising and marketing.
A franchise owner is a complete thrall of the franchisor company, say McDonald's. Everything has to be done in cookie cutter fashion according to the franchisor's rules and specifications, including site selection and building design and layout, product pricing, signage, advertising and marketing, menu, packaging, kitchen and other operations, literally everything. The franchise owner can lose his/her franchise if they deviate from the specified formula in any manner.
In return for being a thrall of the franchisor, the franchisee usually makes money with a proven business model year after year without exercising any independent business judgment about anything. The franchisee is relying on the proven formula, not his/her own independent judgment, to succeed in the business.
The dealer, on the other hand, typically makes a bigger investment, and the dealer relies more on his/her own independent business judgment, although dealers benefit from a sharing of "best practices" amongst their fellow dealers in other locations, and, of course, the manufacturer supports this kind of pooling of experiences because it benefits the company as well as its dealers.