But future plans call for first, initial connection for the message by SMS, then wifi or mobile data (internet, no matter how you're getting to it) for the actual message. And eventually, the initial contact by internet also. (But that's a few years down the line - right now we aren't even taking baby steps, we're learning that there's something called crawling.)
But I expect (not that I'll probably live long enough to see it) that text and voice will be completely internet-based - no carriers at all. (Go back far enough and everything that we take for granted as internet-based - like forums - went via carrier. You called the server - by telephone number - uploaded all your posts, downloaded all the new ones, got off the phone and started reading posts and responding to them. Primitive, huh? Some day needing a "phone carrier" to talk to someone will seem just as primitive. And I'm not talking about the 24th century, Digital communications was teletype machines when I was a teenager. I ran one of the earliest "forums" on a telephone line. So many people on Android Central now may see all communications taking place on some future form of the internet.)