AddEndpointsApiExplorer is for Minimal APIs whereas AddApiExplorer requires, at least, MVC Core. For API projects, AddControllers calls AddApiExplorer on your behalf.
But Why Does Everything Still Work With AddEndpointsApiExplorer?
With the introduction of Endpoint Routing, everything in the routing system boils down to an Endpoint. ASP.NET Core uses the Application Model, namely ApplicationModel, ControllerModel, and ActionModel, to create Endpoint instances and register them with the routing system. Minimal APIs, however, use a builder to directly create and register individual Endpoint instances.
The default API Explorer implementation provides a IApiDescriptionProvider that builds ApiDescription instances from the Application Model. Minimal APIs do not have an Application Model so there is nothing to build ApiDescription instances from. The API Explorer provides these descriptions, which are commonly used by tools such as OpenAPI generators. Without any descriptions, there would be no support for Minimal APIs and OpenAPI; that would be bad (or, at least, certainly not accepted by developers). To address that, the ASP.NET Core team created a second IApiDescriptionProvider that only considers Endpoint.
If Everything is an Endpoint, Why Not Merge Implementations?
There’s two parts to this answer. First, changing the original IApiDescriptionProvider implementation would introduce a public, breaking change. At a minimum, new constructor arguments would be required. Since it was a major version bump, this approach wasn’t off the table, but it turns out to be irrelevant. The bigger issue is that the original IApiDescriptionProvider implementation and AddApiExplorer live in and depend on MVC Core. Minimal APIs only require the routing abstractions. There is no way to merge the two without adding unnecessary coupling. To address this problem, AddEndpointsApiExplorer was added which adds an implementation that only requires an IApiDescriptionProvider implementation based on bare bones Endpoint definitions from the routing system.
If AddEndpointsApiExplorer exists and I call it, do I even need AddApiExplorer anymore? Maybe. The metadata exposed and available on Minimal API Endpoint instances is much lighter than the Application Model; after all, they are minimal. Behind the scenes, a IApiDescriptionGroupCollectionProvider implementation takes a sequence of IApiDescriptionProvider instances. If AddEndpointsApiExplorer and AddApiExplorer are called, then both providers will execute. If only AddEndpointsApiExplorer is called, it will work with regular ‘ol controllers, but the descriptions’ information fidelity might be less than what you are accustomed to. If you are only authoring Minimal APIs, then AddEndpointsApiExplorer is required if you want API Explorer support.
The fidelity between the two methods is improving even more in .NET 7.0. In some future release, it’s possible we might see these approaches coalesce into one.