A server has a static IP address that does not change very often. A home machine that is dialing up through a modem often has an IP address that is assigned by the ISP when you dial in. That IP address is unique for your session but may be different the next time you dial in. In this way an ISP only needs one IP address for each modem it supports rather than for every customer. As far as the Internet's machines are concerned, an IP address is all that you need to talk to a server.
Domain names are strictly a human convenience.
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