are SSH public keys automatically created and transferred with first contact?

so i just sent up an SSH server on my ubuntu server to transfer files between it and my other machines. now when i connected both ways, RSA public keys were created and stored it automatically. i wasnt sure what they were, because i thought i had to generate the key pair and transfer the public keys myself. but there were was a key in the ~/.ssh/id_rsa.pub on the server, a key that i had not sent to that computer... i thought that was weird and i was actually trying to figure how i would do that, i was going to SFTP it over, but then it was already there. am i missing something?

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