How can every single device on a network have a different public IP?

It is impossible for a computer to have the same public and private IP address. It is either a private IP, which is in the range 192.168.xxx.xxx, 172.16.xxx.xxx, or 10.xxx.xxx.xxx, or a public IP, which is any other address.

It is possible for every computer to have a different public IP address. It simply means that whatever establishment you were at purchased the right to multiple IP addresses and their routers are configured to give one to each computer. You could probably even do this at home if you wanted to.

Assuming what you said about every computer having the same public and private addresses is correct, my guess is that every computer has only a public address. All the establishment would have to do to make this happen is purchase the right to multiple addresses and configure their DHCP server to give an address in the assigned range to each computer.

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