The terminology for these systems was never universally agreed upon by the different railroads. Illinois Central referred to its system as ATS, even though it used cab signals. One argument is that both types of systems are technically automatic train stop systems, merely stopping the train if the engineer ignored a warning signal. More elaborate cab signals would continually enforce speed limits, sometimes known as Automatic Speed Control. The Long Island Rail Road was an early main line railroad to receive Automatic Speed Control. And Amtrak's Northeast Corridor has been receiving such a system. But none of the Midwestern main line railroads ever had such systems. The Chicago Transit Authority (CTA) has such a system for its rapid transit trains.
For this web page, ATS and ATC will be used to differentiate between the inductor and the cab signal types of systems. Santa Fe and Chicago & North Western, which have used both types of systems, have used ATS and ATC to differentiate them.