Since badges are completely sold out, but tickets aren't? Is there some kind of mis-communication between companies?

Perhaps they mean 3-day badges versus single-day badges? That's the only difference I can think of.

there are three day tickets too

Where does it say that? I've only ever seen them called badges.

Where are you seeing these tickets? PAX only uses badges that I've ever been aware for attendees, and as you mentioned, those are completely sold out.