Okay let’s try a diagram. Very basic at first.
C1 → R1 → R2 → C2
Person at Computer 1 types 52.38.23.97
into their web browser. This is the internet backbone IP address for one of Blizzard’s web servers for this forum (they have multiple). I went direct IP because adding a DNS server would complicate the example. Packets containing a HTML request, the destination IP, and source IP are sent to Router 1, using its IP.
The packets are received at Router 1. Router 1 has assigned an IP address for Computer 1 to a MAC address for Computer 1. It notes the MAC of the device making the HTML request. It then forwards that request with its own IP but not the IP of Computer 1, along the internet backbone, according to a routing table. Furthermore, the IP of Router 1 changes; it uses one IP to talk to Computer 1 (which is easily changed), and a completely different IP to talk to the broader internet (not so easily changed). Routers creating their own private IP address configurations is called subnetting.
These packets are received at Router 2. Router 2 actually has a completely different IP address, as listed in the previous routing table, but the point is that all packets for 52.38.23.97
come through it, or another Blizzard router. The IP address is known to be for this forum, so it forwards the request to the web server, which does NOT have the same local IP address. It’s a completely different IP address, that you don’t get to know because network security.
The web server received the request, and sends webpage data, as well as the original request, in the opposite direction, first using the local IP address of Router 2, then the internet backbone IP of Router 1. Router 1 then remembers the MAC of the device that made the initial request, which may have changed during this process due to DHCP, and sends the packets to it.
The important takeaway is that every arrow in this diagram represents a completely different set of IP addresses, all of which can be configured in any way desired, and changed multiple times per day, with the sole exception of devices directly connected to the internet backbone. And even those can be changed, there’s just more bureaucracy involved.
And in reality it’s more like
C1→R1→R2→R3→R4→R5→R6→R7→C2
where R5 and R6 are connected to the backbone, R1 is your personal wifi, and R2-R5 are all owned by your ISP.
TL: DR; when you go to Network Settings on your personal computer and see an IP address, that address is only unique or meaningful until you get to your router, past which it is meaningless and no longer unique.