HttpClient registrations
This repo contains a bunch of code to figure out how registering HttpClient really works and how IHttpClientFactory fits into that.
If you look in the http folder you'll find a console app that registers a basic client class TestHttpClientA (and B, C and D) that make a simple HTTP GET call.
They are registered in four different ways and when their Execute() method is called dump some info about the hash codes of the HttpClient instance and the handlers that this particular HttpClient has and their hash codes.
This should allow us to see what the difference is between the ways of registering a HttpClient and what you get at runtime.
To test this the app will simply resolve each type four times in a loop and make a call.
Output is like:
[08:40:44 INF] TestHttpClientA => 37251161
[08:40:44 INF] Inner Handler Microsoft.Extensions.Http.LifetimeTrackingHttpMessageHandler => 66824994
[08:40:44 INF] Inner Handler Microsoft.Extensions.Http.Logging.LoggingScopeHttpMessageHandler => 64554036
[08:40:44 INF] Inner Handler http.TestHandlerA => 44115416
[08:40:44 INF] Inner Handler Microsoft.Extensions.Http.Logging.LoggingHttpMessageHandler => 61494432
[08:40:44 INF] Handler System.Net.Http.HttpClientHandler => 16578980
This'll be repeated 4 times for each type, the interesting bits are the first and last line. HttpClientHandler is the inner most handler and, according to docs, the one that is managed by the IHttpClientFactory. The first line is the typed client that either consumes HttpClient of the factory (look at the different types to see which).
Sample of a full run can be found here
The short of it: It doesn't matter how you register.
However it does matter how you resolve, if you resolve a typed client and keep that in a singleton you'll keep using the same HttpClient and HttpClientHandler.