Accidentally commented on a subreddit I was banned from another account. Quickly deleting it still didn't work. The mods reported it to the admins, thus you know.
Reddit collects a lot more user login data than you think. They most definitely know exactly what unique machine you're using to log in regardless of IP.
I've often wondered how this works when people use generic computers like macbooks. I've been banned from subs before but because I make a new account like once a year I just end up back there commenting eventually and I haven't ever been banned again.
Out of 2,000,000 fingerprints my browser is unique (well, I do use Firefox). So in theory a website owner could identify me just based on that. No IP needed.