There are multiple shipyards. As I understand it (anyone feel free to jump in here and correct me if I'm wrong) the shipyards are not run by Starfleet. They are all independent businesses that contract with Starfleet. They all come up with design proposals, independent from each other, that they trot out in front of the bigwigs at Starfleet, in hope that their shipyard will win the contract to build multiple copies of their design to bring the number of ships in the fleet up to the level that Starfleet wants. Let's say that Starfleet tells two or more shipyards, "We want a full-scale, working prototype of your heavy cruiser design that we can test in field trials." Each shipyard builds up a prototype and puts it in the hands of Starfleet for testing. At some point, Starfleet makes a choice from among the prototypes. The non-winning shipyards set aside their prototypes. Starfleet does not require them to be destroyed, because they don't include sensitive, advanced tech that Starfleet would have added on later. Along comes something like the war with the Klingons. A large percentage of Starfleet's ships are destroyed. They can't be quickly replaced. What would be a quick go-to source for some ships to help fill in the gaps? The unused prototypes. It's not difficult to imagine a scenario in which the Disco Enterprise was the design that Starfleet chose initially for regular production. The TOS Enterprise design might have initially been a non-winning competitive design. If the Disco Enterprise for some reason turned out to be hopelessly defective, or chronically troublesome, or whatever, Starfleet could easily transfer the name and registry number to the TOS design and have more built based on it. There is a bit of precedent, in a way. After Challenger was destroyed, there was a proposal to refit the space shuttle Enterprise into being a fully-working orbiter, as a replacement. It was finally decided that the costs involved and the work it would have required made it more practical to simply build a new one from scratch. But, it was seriously considered. Granted, the design itself was the same as the other orbiters, but I think you see the parallel that I am making here. Design studios have been known to cabbage details from competing studios, to varying levels, when opportunities present themselves. That would account for similarities in some design elements. So could Starfleet saying that they wanted to test variations on a 'theme' or general design parameters. Potentially, Starfleet could even approach one particular shipyard with a request for two separate prototypes that take a design in two somewhat different directions. I feel that this idea could even work in the case of the Klingons. Different houses with different ship designs. Or, even in the case of unification of the Klingons, different shipyards operated as businesses that contract with the Klingon government. This could explain why the ships in Discovery don't match the ones in TOS. And, keep in mind, this is the future. It might not be as costly and involved to create a full-scale, working prototype in the future as such things are in our here-and-now.