That is correct. The picture will be scaled to fit in a given resolution.
It might not be the same picture though. Like when the movie's resolution is greater than the projector's. It makes sense that detail, or call it resolution, will be lost.
Using a 1280x720 resolution movie as an example, a projector set at 800x600 will have to throw away a lot of information, since it's new job is to display 921,600 pixels (1280•720) with less than half that available to it. The 1280x800 setting can comfortably fit everything in its workspace.
Still though, for projecting movies, the thing that matters is up to you when you're sitting in your seat. If you have a 4:3 screen that can only accommodate 1280x800 by shrinking the image far beyond the size of how 800x600 compensates with the movie, then maybe 800x600 is better.
But if you're talking about details, and not cropping, it matters a lot.
If you cross your eyes while watching the movie, is any information lost? – Michael – 2015-02-27T17:15:00.053
Color rendition can have as much impact to perceived picture quality as spatial resolution. The ability to notice the picture details will depend on the source material, viewing distance and your eye sight. The emphasis on a display's resolution is driven by TV marketing hype. There's always a specification de jour to sell new TVs. Nowadays it's "4K", and previously it has been "480/240/120Hz" (refresh rates), "3D", "LED" and "1080p". – sawdust – 2015-02-27T20:03:26.050