Sometimes this happens: I'm going to assume that you're telling the truth since I've got no way to check.
My assumption is that a staff member did /getalts or /ipcheck when GeorgeTheFatCat was banned. This command brings up a list of players that have used the same ip; it's supposed to speed up the ip check process but it's definitely prone to error.
Staff will want you both on discord to prove you're two different people. That is flawed as well for many reasons but mostly because it relies on a banned person to be actually willing and able to help you out.
My memory is a little fuzzy but there should be a better way for staff to check. They can do a prism lookup for your log ins [/pr l a: player-join p:TTae,George r:global t:whatever] and that should show the exact ips that each of you log in with. If you're both consistently on different ips then it should be proof enough to unban you. They can also do /pr l a: player-join k: (TTae's ip) p:George r:global t:whatever to see how often George is using your ip address. If it has only happened once or twice it seems unlikely to be your alt.
Since I can't post on your appeal I'll just tag @Flamedemond2
Again my memory might be wrong but hopefully if you're innocent we can get it cleared up without relying on George.