Broadly speaking (many exceptions), Americans are fine with young teens watching a movie about a man using kung fu fantasy tactics to bloodlessly shoot his way through a building of bad guys, like John Wick, but don't necessarily feel the same way about something that depicts violence in a more brutal and arguably realistic way, like Saving Private Ryan. Is there a little puff of red CGI mist blood coming out of somebody's chest, or does the movie show one of the 'good guys' with half his skull blown away? These are both hardcore violence in a sense, but most people see a large qualitative difference between the two.
I think it basically comes down to how likely a movie is to give people nightmares, which of course is a function of desensitization. The American public is broadly desensitized to unrealistic violence, but most aren't desensitized to realistic violence.
Incidentally, Saving Private Ryan has a lopsided depiction of violence. The deaths of Americans are shown to be gruesome and agonizing, while the deaths of Germans are mostly shown to be relatively quick and clean: https://www.youtube.com/watch?v=l4FeyONCtfc I re-watched Saving Private Ryan after watching this video and found it to be very apparent, but it wasn't apparent to me the first time I watched it.