Games are usually made somewhat like this:
One part of the program models and simulates your game world, using arbitrary units for measurement. That's world space.
This game world is viewed through some sort of camera (possibly multiple cameras).
The HUD/GUI is drawn on top of what the camera shows, using another set of units (pixels are an option). That's screen space.
When you switch resolutions, the shape and size of your screen space changes. The GUI may have to adapt -- it is your choice whether the GUI elements scale and/or reposition themselves.
World space, however, is unaffected. You only have to adjust the zooming level of your camera to an adequate value. The simulation still works with its usual units, and the camera maps them to screen-space coordinates.
Edit: I see that you've already touched this concept in another answer, so I'll hinge on that. You're spot on with the "virtual position" vector: that's your world-space coordinates. The only missing piece is that one world-space unit does not have to equate one screen pixel: you can very well simulate everything in meters, then the camera maps 1 world-space meter to 32 screen-space pixels, so a one-meter object takes up 32px on-screen.