Generally speaking, secondary (or tertiary, or...) displays can either be set up as duplicates or as additional displays. What's actually going on in the internals is mostly irrelevant, because the behavior is configurable.
When you're duplicating displays (perhaps driving a projector or a television), both displays have to show the same thing. You will be limited to the characteristics of the "worse display" - particularly the lowest resolution. You may get clipping, you may get distortion, depending on the display device. Either way, it's a setting that's adjustable. You pick a resolution that's most compatible with both devices.
When you're using it as an additional display, the biggest problem you'll run into is practical: the potential for differing physical sizes as you move windows from one to the other. A window that's 504px × 300px is going to be the same number of pixels on either screen, but depending on the difference between the resolution and physical sizes, the window could be physically larger or smaller when moved from display to display and will use a different portion of that display.
Personally, I have one machine with three displays - a 30" 2560×1600 and a pair at 20" 1600×1200. It just so happens if I turn the two smaller displays portrait (making them 1200×1600) the math works out that the pixel height of all three displays matches the physical height. Even better, because they're all the same same product line from the manufacturer (Dell), the bezels are all the same size, too:
A couple of my other machines have two displays, and I always buy them in matched pairs so I don't have to deal with any of the geometry strangeness. I generally avoid running a laptop with an additional, mismatched display - I prefer identical displays or carefully selected groups. There are portable solutions that may match a laptop more closely in both resolution and physical size.
A third option is using just one display. Most laptops can be configured to turn of the display but remain powered on with the lid closed. You could just plug in the secondary monitor, set it as the primary display, and close the lid.
The video hardware of the machine will have a maximum resolution it's capable of. That's the biggest determining factor in what the "best" display for the system is, assuming resolution is best. There are arguments to be made based on use case - sometimes you may not care about resolution, but simply want raw size. The Jumbotron video board in the AT&T Stadium is/was 72 feet tall and 160 feet wide, but only HDTV resolution (1920 x 1080) - each pixel was a inch across.