If you are within the network, like at home, every computer has its own IP address. So your server at home could be 192.168.1.10, your laptop could be 192.168.1.11 and your desktop could be 192.168.1.12. If you go to a website like gatebot.com on all three computers, it shows you ONE IP Address... the external one from your ISP. So if you were trying to access any one of those computers from the outside world, you would type in that one IP address and from there you could be routed to any one of those computers using ports.
Back to your question, the recipient will most likely see the ISP IP address (the external one) or the domain name pointing/associated with it.
Also, if the server hosting your website is not in your network, your ISP's IP address will differ from your domain name / server.
~Sovereign
Is the ip address that was given to you by your internet service provider different from the ip address of your domain name hosted by a server? If I send an email using a mail server, what is the ip address that the recepient will see? A mail server has it's own IP right?

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