How is a higher resolution video stream displayed?

Question

Video

If the video is in 1080p, and it is played on the monitor in 720p, will the picture be different from the option when the video was converted to 720p beforehand? If so, what and in what direction.
What happens when you play a video with a higher resolution? After all, the conversion requires more resources than are consumed when playing such a video, where something happens in real time.