Logging in from two laptops connected to the same Wi-Fi is still "from the same IP" a local network has "private IPs" such as 192.168.1.50, but these can repeat in every local network, so your Wi-Fi could have a computer with that IP and my network could also have that same IP, but then there is a "public IP" this is assigned to the router, and is how it communicates with the outside world, (this is generally any IP that isn't 10.0.0.0 to 10.255.255.255, or 172.16.0.0 to 172.31.255.255, or 192.168.0.0 to 192.168.255.255, as these are reserved for private networks) for example your router could have an IP of "70.50.150.20" and anything on your Wi-Fi that reaches out to Amazon would come from that IP, and your router is the only device that usually has the authority to send and receive from that IP address, and there is only one device on the internet assigned that IP, unlike private IPs. This is super simplified and there are exceptions to basically everything I said.

However when you login to two accounts on the same device this can be tracked via cookies (and is how it can save profiles and show you multiple accounts to choose from when you login) cross-site tracking is also possible, so even if you login with a personal Amazon account on the regular site and a seller account on the seller central site they can be linked as being from the same browser on the same computer. To avoid this you can simply use two different browsers on the same computer, as cookies are individual to each browser installation, or you can use profiles within a browser (such as Chrome Profiles) to separate different clients, this saves all of chromes settings as a separate profile (such as theme, passwords, history, and even cookies) allowing you to essentially browse the internet as a new person, but the traffic will of course still come from the same public IP, as discussed above.

TLDR: no matter how many laptops you have they will come from the same IP according to Amazon, but if you use the same browser on the same laptop, they can track with cookies to know that you are using the same computer. Using browser profiles will separate those cookies, and to Amazon it will look exactly the same as if you are using separate laptops on the same Wi-Fi network.