There is a difference in PrintScreen and Win+PrintScreen on normal Windows. The first copies the complete screen to the clipboard the second also saves it to your pictures-folder. The second only works on Windows 8 and higher.
So:
PrintScreen = Makes a screenshot and saves it to your clipboard
Alt+PrintScreen = Makes a screenshot of the current Window and saves it to your clipboard
Win+PrintScreen = Makes a screenshot and saves it to your pictures-folder
(There is no equivalent function to save the current window to your pictures-folder.)
With the Surface Pro 3 these function are reached via:
Fn+Spacebar = Makes a screenshot and saves it to your clipboard
Fn+Alt+Spacebar = Makes a screenshot of the current Window and saves it to your clipboard
Fn+Win+Spacebar = Makes a screenshot and saves it to your pictures-folder
(You can verify this by pasting in Word or Paint directly after using these functions.)
Edit (a bit off-topic because it's not native Windows but you asked for alternatives):
You could, as an alternative, use GreenShot. It has the ability to capture a window, a region and full screen with programmable function keys. It also has an editor and the ability to upload directly to imgur.com (which is really nice on sites like superuser.com).
I can't test this but: FN + Space = full screen and Alt + FN + Space = active window – Rik – 2015-02-03T22:02:50.793
@Rik The first combination doesn't work on my system. The second, neither. Did you forget to add Win key, there? If so, the first one would work but the second still fails to produce the needed behavior. More suggestions? – Konrad Viltersten – 2015-02-03T22:34:57.450