Original question - it depends on how your graphics card drivers are set to act. Usually if you set a specific resolution in your game the graphics card switches to that resolution displaying everything in it, if you alt tab to desktop the resolution will change to the desktop resolution again, or not depending on how your drivers react. Some will only go back to the original desktop resolution after you exit the game.
Native resolution is the resolution of your LCD screen, it has nothing to do with your graphics card which doesn't care what resolution you would like your games displayed in unless it's something too big to handle (too many objects to render at a specific time/not enough texture memory).
As you probably know LCDs have a fixed amount of pixels. You SHOULD play in your native resolution because it looks much better - every single pixel your graphics card sends to your LCD monitor gets displayed as it should by corresponding pixels on your LCD panel. If you launch a game in a different resolution your screen tries to adjust but considering that it can't divide a pixel into smaller parts (duh) the image will look bad, not sharp. It doesn't force your graphics card to work harder though. It's just your display trying to work out how to display a different signal that your GPU sends, the GPU doesn't give a shit because it did its job which is to send a signal that you wanted it to send. Actually smaller resolution means less objects to render, which means less work for your graphics card but it will look like shit because of how your LCD acts.
Back in the CRT display days it didn't matter, a smaller resolution meant bigger pixels and that's it, because it didn't have fixed pixels. LCD does. That's why if you want your image to look fine and sharp you should display it in your LCD's native resolution. The second acceptable resolution (sharp but pixelated) would be quarter of your native resolution - that way 4 pixels work as a single pixel.
Now you can't display a higher resolution than your screen's native resolution simply because it wouldn't make any sense and would only force your graphics card to work harder. You can't display more pixels than your LCD technically has.