also, are they even really "modems"? I know that "cable modems" are really routers… surely cellular modems aren't all bzzzt-brrzzt-bing-bong-bing-bong like my 90's Hayes 1200baud.
Yes they are. Modem is an abbreviation for MOdulator-DEModulator which is what they do, they modulate and demodulate radio signals to digital and vice versa.