Color Grading is the term you want. However, a lot of people do use the terms color correction and color grading interchangeably.
Technically, color correction is getting elements or shots to match each other and color grading is creating the overall look of the piece or scene.
A lot of this has to do with the cameras that are capturing the scene in addition to color grading in post. You need a camera with a wide dynamic range to get that kind of look or a lot of control over the lighting of the scene.
Or, ideally, both.
If you shot something with a camcorder or a smartphone, it's not going to look like this unless you put a lot of work into the lighting beforehand. And the shallow depth of field only happens with certain lenses.
I would like to direct you to THIS video:
Look at how many people are involved in the shoot. Look at all the professionals from various disciplines. Look at all the rehearsal. Look at all the painstaking attention to detail. Look at all the professional equipment they used.
Yes, I looked at the shot at 1:32 in the video they made. They used a Steadicam to stabilize the camera going up the stairs. They used gels on the window to reduce the light intensity and help correct the color temperature. The interior spaces of the upstairs and downstairs have also been lit to avoid irising problems. They didn't rely on mere chance.
Did you also notice the subtle cuts at 00:38 and 1:54? That video was not shot in one take, and that's a fact. And before they even got to the step of color grading, they KNEW they had good video to work with because they had the professional experience to attain it.