A public key is meant to be shared with anyone who is the recipient of data encrypted with the private key.
So the private key resides on the server and should never be shared. Data leaving the server is encrypted with the private key. This data can only be decrypted with the public key.
The public key is easily downloaded and made available to anyone who the owner of the private key wants to have access to it. Which is usually everyone. The public key decrypts the message that is encrypted with the private key. It also encrypts the data on the way back to the server. This data can only be decrypted with the private key that is paired with the public key.
So they are a pair. They work hand in hand with each other. But one (private key) is designed to never be shared with anyone while the other (public key) is designed to be given to the recipient of the data encrypted with the private key.