60hz content on 50hz display?

[CuriousGamer]

I was having a discussion with a friend of mine recently which got me thinking about 60hz devices such as games consoles and computers on 50hz displays like TVs in PAL regions.
When I had my old CRT TV I know it had a 60hz mode for NTSC and PAL 60 but with HDTVs I can't find how things work.
For those that don't know HDTVs in PAL regions have a base of 50hz, instead of the base of 60hz in NTSC regions (100 vs 120, 200 vs 240, etc)

My question is what refresh rate does they use for 60hz content and if it's not 60 what happens to the video stream?
My TV tells me what the input is, 24 for Blu-Ray, 50 for Sky, 60 for consoles but how can I be sure that is what is being displayed?

I've tried searching for an answer but get stumped when someone comes in and declares 50hz displays a myth.