PTC is a sort of form of ATP, but installed as an overlay on whatever existing system is already there rather than integrated into the signal system. It doesn't meet the traditional definition of ATP because of that, but still performs largely the same functions.PTC and ATC are part of the spectrum from ATP to ATO, which describe different levels of automation.
ATP is Automatic Train Protection. This is just a traditional signal system which monitors the train and intervenes if it violates any signal aspects (e.g. overspeed, passing red signal). I'm not familiar with the American PTC standard, but I believe it is a form of ATP.
It should be noted that neither PTC nor ATP are by themselves signal systems. PTC is an installation on an existing signal system, while ATP is a function that can be built into it.
It should also be noted that there does exist at least one signal system in the North American sphere of operation which meets a lot of what people envision as the requirements. Amtrak's ACSES isn't a moving block system, but allows for virtually all of the same functionality of an ETCS Level 2+ installation.