The screen resolution is the same but the resolution of the image can change. If a system's output renders to the entire screen then just imagine a 1 pixel output would make the entire screen the same color. 4 pixels could have 4 quadrants of colors. 16x8 pixels would have 128.... etc. The max resolution would be the max resolution of the display. Though a topic of interest may be sub-pixel rendering where a system/font/game can take into account the RGB color pixel layouts in an LCD screen into account in order to improve the visual quality of the max resolution.

So a system can have double the resolution of another and games can even choose to render at different resolutions depending on how intensive it is. Some games will choose lower resolution but more polygons and some might choose higher resolution with fewer polygons, among other choices. There are even modern cases where console games will change the resolution they run at to keep framerates solid https://www.halowaypoint.com/en-us/forums/6e35355aecdf4fd0ac...