Cellular cameras are basically cell phones in trail camera bodies. They communicate (send pictures and status reports, receive commands) over the same cellular networks that cell phones use. The communications are routed through a server before being transmitted to your phone or mobile device (using its carrier) or computer (via email and/or your ISP connection). The cell camera does not “talk” directly to your phone, mobile device, or computer.
The cell camera uses its cellular carrier and your phone uses its own cellular carrier. They can use the same cell carrier or different carriers, just like the people you call and text can use the same cellular carrier you do or a different one.