As a practical matter, in LAYOUT, which max-width should I use in order to correctly size a web page?
I read that these sizes are the most used currently:
1920×1080 (9.94%)
1366×768 (6.22%)
Does it make any difference if I choose 1366px max-width and display the page on a 1920px wide screen?

If you set the max-width at 1366px, the width of the content of the site will max out at 1366px. If you’re viewing on a 1920px screen, then the other 544px (split on either side) will be the page background (Background tab).

I set my max-page width to 1280px for a couple of reasons. One is that it just seems big enough. I also took into consideration how text would look on a page. I don’t want visitors to have to scan across a wide monitor to read text.
So I use 1280px for the overall width, 1280px for Main Copy width, and then 24px of left/right padding in the Content Areas of the template.

On wider monitors, there is more page background area. I’m ok with that.

Thanks Rod

I suggest not choosing a max-width larger than the screen or window you’re working with. Also, how text-heavy is your site? Tracking text across 1366px pixels is very uncomfortable for most readers, which is why the majority of blog-type themes sport widths less than 1000px. There are plenty of design articles on this; here’s one, selected at random.

If you’re just doing a thumbnail grid, then you can set a larger width. If you’re writing essays, then you may want to favor narrower content areas.

Thanks, Matthew,
In fact, this is an update of the site which was a bilingual site based on two sites, French and English, built side-by-side in parallel.
I am now upgrading the site to use the language switch: It’s on a sub directory while I tinker with it.
Rod suggested I use 1280px wide. I’m trying it out. Almost done.

1280 is just what I use for the page width. Most of my text areas are narrower than that, either in columns or with an image that makes the actual reading width much less than the full width.
I have a few pages, mainly sets and albums, that use 1280 (minus padding), but those are just maybe a couple of short paragraphs. If the text is much more than that, I’ll break it into columns.