My experience is in the US. PTCRB is the standardized one. Even on top of that, AT&T has additional testing (see TRENDI, which is a whole lot better than what they used to require). Verizon has their own idiosyncratic process where you don't learn what standards you need to meet until you submit a request for testing.

The carriers don't use technical measures to keep uncertified devices off their network. It's still usually a violation of the terms of service. And yes, that means that aftermarket PCIe-form-factor cell radio in your laptop is theoretically a problem unless that precise laptop + card combination has been certified.