Assuming the question is legit...
The FRA pages (more than just the one linked, look at all of them if you want the details) describe what the law requires for PTC. There are several ways to do it. Amtrak uses ASCES in the NE Corridor and Incremental Train Control
on higher speed lines between Chicago and Detroit; both are considered PTC. "PTC" in common usage these days, though, usually refers to the form being installed on freight railroads.
Freight railroads need a form of PTC that is interoperable between multiple railroads (including Amtrak long distance and regional operations, and commuter lines running on freight railroads), which has turned out to be a fairly tough nut to crack but is now being implemented. The primary focus is on passenger and certain types of freight operations. Several commuter lines are now operating under PTC on all or part of their systems.
The older ATC and ATS systems are not PTC, though they do in principle, at least, address certain aspects of PTC.
In rail transit (fully separated from public access except at stations, and not on freight railroad lines), the ATC term can refer to fully automated train control where the driver (if present) monitors operation, can respond to emergencies with a manual override (perhaps with significant operational limits, as on BART), and may be able to override certain things in normal operation (like door closing). Major systems that are fully or mostly automated include (but are not limited to) BART, Vancouver BC's Skytrain, and (if enabled) Washington DC's Metro. Transit ATC is not PTC.