Presume I create a new key, then calculate a public address from that key.  So far, it is just on my computer and is not what I would call a real address.  If I then send some coins to that address, does that automatically create the address in the real bitcoin world?  Maybe I go to Gemini and enter that public address as the receiving address and move some coins.  Does that result in the new address being created?  Are there other methods worth mentioning?

I suspect, that new addresses are created, in the real BTC world, when some amount of coin is sent to the address.  Is there more to it than this?