I am confused by your reply.
>>I believe it works for all models
I know I can select a different model in the simulator and test my game application on the simulator, however, my question is why different models selected on the simulator do not connect to my personal "real" iPhone 8 phone.
>> ...but the simulator never receives notifications from Game Center
I understand sending/receiving Game Center "invites" does not work on the simulator. This is not my issue though.
Here is an example of my issue, hopefully explained more clearly:
1) Select "Iphone 11" in the simulator, then start running my game application in the simulator.
2) In my game running on the simulator, select to "Host" a 2-player game, then select "Play Now" on the Game Center matchmaker View Controller, which is displayed, so it can go off and automatically find one other player to play my game. It is now spinning looking for an available player.
3) On my personal "real" iPhone 8 phone, I start my game application and request to "Join" a 2-player game.
4) The game running on the iPhone 11 simulator and the game running on my iPhone 8 never find each other so the game never starts. Each keeps spinning/looking for a player to add OR a game to join.
** If I perform all of the steps above again but use "iPhone 8" model on the simulator then everything works fine and the simulator and my real iPhone 8 model join together and can play a game successfully.
Basically, if the iPhone model selected in the simulator is set to any model other than "iPhone 8", then it will never automatically find my personal iPhone 8 phone to join to the game. This makes me think that the simulator iPhone model must match the "real" iPhone model being used for testing for Game Center to find players.
Any ideas why the simulator must be set to iPhone 8 model in order to allow it to set up a game with my real iPhone 8 phone?
(EDIT)
In addition, I added the "iPhone 8 (12.4)" simulator to Xcode. When I select "iPhone 8 (12.4)" in the simulator and try to connect to my real iPhone 8 phone (running iOS 13.3), then the simulator and my real iPhone cannot find each other. If I select "iPhone 8 (13.3)" in the simulator then the simulator finds/connects to my real iPhone 8 (with iOS 13.3) phone and starts the game. So it even seems the simulator iOS version has to be the same as the version on the real iPhone being used for testing as well.