I can't tell at all when my mbp is in 120hz or 60hz. I tried to set up a good test too by scrolling really fast while plugging and unplugging the power adapter (which kicks it into high power 120hz or low power 60hz).
I also use 60Hz screens just fine, saying that getting used to 120Hz ruins slower displays is being dramatic. You can readjust to 60Hz again within 5 minutes. But I can still instantly tell which is higher refresh rate, at least up to 360Hz.
Most people who’ve used both 60 and 120 could tell, definitely if a game is running. Unless you’re asking me to distinguish between like 110 and 120, but that’s like asking someone to distinguish between roughly 30 and 32.
North of 120 it gets trickier to notice no matter what IMO.
I can live with 60 but 85+ is where I’m happy.
On a perfect display you should see just a faint grey circle.
Another test is moving cursor fast across the white page and tracking it with eyes. On a perfect display it should be perfectly crisp, on my display it blurs and moves in steps.
So basically on a perfect display you can track fast moving things, and when not tracking, they are blurred. On a bad display, things blur when tracking them, and you see several instances otherwise. For example, if you scroll a page with a black box up-down, on a bad display you would see several faint boxes overlayed, and on a perfect display one box with blurred edges.