Basically, the IP address is the internet address of your computer. Every time you connect with your ISP, your computer (or router if you have more than one Computer with internet access) gets assigned an IP address to communicate with the rest of the world. ISPs usually have a range of IP addresses to assign to their customers, thus it is very rare that two different house addresses get assigned the same IP address (unless in certain cases, but we know how to handle those).
Ya forget the details when you run too many spaces...
I was thinking of your typical university environment where all the dorms are behind the same DMZ/Gateway/DNS space. If your gateway matches a friend and the DNS server is the same I'd register multi for sure. If you have a personnel router you'd have to look at its settings...
E-mail your isp provider and ask them how they work
very politely dm multi accounts and tell them you don't know if your isp has you sharing, and if so, please let you know with whom so you can arrange to multi account with that person/persons.
I would only recommend the last if your isp is an ass about telling you it's IP number assignment policy.
Most ISPs function in the same way. The exception is that a handful of ISPs display all their users as behind the same proxy, but SWC distinguishes that, and those users don't need to register, since they would need to register with every other person using that ISP at all.
So the easiest way is just to ask any SWC assistant, instead of pestering your ISP and trying to interpret what they tell you. We can check your IP address, we can check if you're using a proxy, and we can compare the IP between two accounts.
The general guideline is that you need to register if you are using the same immediate connection as another SWC player. This means if you share a computer, or if your computers are networked and connect through the same router, you need to register. If neither of those are the case, and you never share a connection (meaning you never log into SWC from the other person's connection) you don't need to register. It is pretty straightforward.