Yes...ish. Depends on how you have your network set-up. If you have a router there is the public IP and the NAT (localized). When connecting to the router you are connecting to the NAT (192.168.0.1 or 192.168.1.1 for most home based routers), which in turn connects to the internet via the unique public IP.
Computers on the network have IPs (NAT in this case) that are close but not the same. My computer as assigned by DHCP is 192.168.0.196 and my sister's as assigned via DHCP is 192.168.0.195.
In short, with a router your public IP is the same, but in your network you connect to the same one and are usually assigned one; if not assigned you connect as a static IP on the network.
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