What happens when I display 1080p video on a x720 resolution setting?

This one puzzles me, and I'm looking for a very technical answer.

Say I'm on YouTube and I chose 1080p for the video resolution.
However, my screen's resolution is 1280x720.
This means I'm displaying 1080 on a 720.

Is it possible for the human eye to notice the difference?
Is it the same as if I just changed the video's resolution to 720p, making 1080p resolution a waste if I didn't have the display resolution for it?
Is it actually worse to scale down a 1080 video to a 720 display? Does it pixelate or something?

I honestly don't have good eyes to test it myself, and that's why I'm looking for an impartial, technical answer.

Thanks.

2 Answers

Although from a technical point of view, people would say you cannot see the difference, I have found this to be incorrect if you use Youtube as example.

You can indeed see the difference, but its very hard. A 720p quality is already good, but because of the scaling down from 1080p to 720p on the fly, it is possible to see a quality increase. This is mainly due to how movies are compressed at youtube. Youtube's attempt to trim video's from 1080p to 720p remove certain details that your monitor doesn't. This is solely a compression thingy though, but it can be seen. Even better way to see the difference is to play a QuadHD: 4096p video on a 1080p screen and compare it to the 1080p equivalent.

If you keep youtube out of the loop and look at movies specifically compressed to these formats without any data loss, technically speaking, you won't see a difference.

Although the comments are correct, the simple answer is your browser, player, or other piece of software just scales the video accordingly to fit the screen. If you are playing a 1080p video on a 720p screen (1280x720 or 1366x720) than you are just wasting bandwidth and potentially will get more buffering. If you are only capable of displaying 720p video, using a 1080p stream is just a waste for the most part.