When a display (LCD, LED, OLED, etc) changes its display resolution, are pixels on the display "turned off"? Meaning, are the same number of pixels on the display being used to show an image with less detail, or are fewer pixels being used on the display itself?
It depends on the monitor, and the resolution. Older LCD monitors always used their whole final display area, so that if you had 960x760 on a physical 1024x768 screen, the "logical" pixels (of which you have 960x760) would appear slightly distorted and blurry, and the picture becomes clear only if you use an integer submultiple of the physical resolution (e.g. 960x540 on a 1920x1080 monitor).
More recent monitors still have this mode of operation available, of course; but they often also can "adjust" the output so as to improve image sharpness ("underscan"). If the logical resolution is slightly less than, and close enough to, an integer multiple of the physical resolution, the physical resolution is "lowered" as needed by adding a black border of unused pixels; then the image is resized.
This way, a 920x512 resolution would be scaled to 1840x1024 and displayed on a 1920x1080 monitor by adding 40 black pixels on either side, and 28 pixels top and bottom. Each logical pixel would thus exactly fit 2x2 physical pixels, giving very sharp image edges.
Such monitors also have a "TV" or "Video" mode in which either this option is disabled, or an antialiasing stage is added afterwards (e.g. Samsung).
For a twist: Windows has a special trick it plays with LCD screens, adding fake colours to pictures so as to give an illusion of added smoothness when the picture is displayed on a LCD screen (this is known as "ClearType" technology). ClearType has to make assumptions on the LCD grid structure (even if it can be configured, up to a point), and usually it plays merry hell with the newer monitors' "Computer" mode, resulting in text growing coloured halos, e.g. between the legs of m's. In such a case, either adapt the computer output to the monitor expectations (disabling ClearType) or the monitor to the OS's expectations (using a resolution that exactly matches the physical available resolution). Turning the monitor into 'Picture' mode may then help somewhat.
If you decrease the resolution, then you have fewer points drawn over the same amount of physical pixels. If you increase the resolution then you have more points drawn smaller over the same amount of pixels.
So for a 200 * 200 screen, if you decrease the resolution then a 100 * 100 box could still be 100 * 100 points, but each point is painted at 2*2 instead of the standard 1*1.
This depends entirely on how the monitor and the graphics card are configured.
I.e., I can configure my graphics card to stretch smaller resolutions to fill the entire monitor, as AthomSfere described. I can also configure it to simply center the image on the monitor, leaving the unused pixels black (the concept of a pixel 'on' or a pixel 'off' varies from technology to technology with LCD / LED / OLED).
Some monitors also allow you to set this kind of behavior on the display itself, for when it's receiving a resolution lower than it's native resolution.
To additionally clarify, the pixels on LCD/LED/OLED displays are fixed in position. If the resolution is lower than the native resolution, and it's stretched to fill the screen, those pixels don't move to take up the extra space. Rather, the digital circuitry either in the monitor or the graphics card is upscaling the resolution to the monitor's native resolution, and this is why LCDs look terrible when they aren't running at their native resolution.