HDMI, the link is 99.99% of the time going to send out about 60 frames per second. Yes it supports 24, 25, 50 and of course 60 frames per second so if you get an 120 Hz display (another way to write 120 frames per second) what is going on?
The answer is not sure. Some monitors simply show the frame 2 times and we are back to 60 FPS but on scree 120 FPS. WHY IS THIS!!!!? Because LCD panels are mass manufactured so to get the cost down you use what you can get on the market and tweak the electronics to match. You also get to sell this as a feature.
The next thing that could happen is MOTION SMOOTHING but gamers tend to dislike that since it can create INPUT LAG. Google INPUT LAG if you need to catch up. Motion smoothing is hit and miss from what I see. Some folk like it as the monitor or TV tries to make up what the new frame could be from one frame to the next. But there's the reason for INPUT LAG. We have to wait for the next frame before we can display the prior frame with smoothing.
PS. Edited for spelling.