I just accidentally hit cmd-` (the key to the left of the "1" in the top number line) and it did something.

It looks like it's doing a "next window". I wasn't able to find any menu option that shows that as its shortcut, nor could I really find a "next window" menu option. (hotkeys almost always trigger a menu entry) shift-cmd-` also works as previous-window, a bit like the next-tab hotkey.

Works in Safari and Mail, it appears to be system-wide.

I don't know about systemwide, but look under "Window" in Finder.

Hmmm... I can't get it to work in Safari. What did you do?

I got Command+tilde (⌘`) to work in Safari 11.0.3 — once I realized it meant "Cycle through WINDOWS" and not "Cycle through TABS"

This is hardly new. Command-tilde cycles through windows in pretty much every app I can think of, and I've been making use of it at least since Mavericks.

In fact, the first reply to this fifteen-year-old hint seems to indicate that this behavior was instituted in OS X 10.2 Jaguar.

Tabs or no tabs, it wouldn't work for me until I had brainstorm, went looking, and found that this unchecked box was my problem. (10.12.6, anyhow)

FWIW, the default setting for that PrefPane is to have them all checked, but NOT have the checkbox marked for "Change the way Tab moves focus" (the one in the upper left corner....)

You're right, and I'm guilty as charged.

I've got a nasty habit - particularly nasty for a bartender - of moving my hands very quickly without particularly looking at where they're moving, as a result of which I knock things over...and hit unknown key combos that cause all sorts of weird things to happen on my screen without my knowing why they've happened or how to recover.

To mitigate that, I turned off all seemingly unnecessary combos, command-tilde having been one of them (until now that I see that it may be useful to me), and promptly forgot about them.

Interesting... but why isn't it listed in the menus?

It's listed under Finder > Window, but that's it as far as I've seen.

None of the commands in that pane are listed in menus, maybe because it would make them too unwieldy. I've got no idea why command-tilde was deemed so important in Finder that it's listed there.

Thing is, from my programming background I've found that to GET the shortcut at all you have to add it to the window object, and doing that also automatically adds it to the menu. You can't just get the function without it showing in the menubar. (technically, the shortcut doesn't "do" anything, it triggers a menu option, which is what "does" the work) So I have no idea why it works other places but doesn't show up.

Trying to stretch my imagination here, and it keeps snapping back like a rubber band.

One thing is the Finder command, "Cycle Through Windows", differs from the System Prefs command, "Move focus to next window", and that suggests that the commands differ in some way despite the fact that their functionality is apparently the same.

Could it be as simple as the Pref Pane commands having been coded into invisibility to avoid menu bloat? (The modifier keys don't change the menu's behavior.)

That's basically my guess too, that the window cycling behavior is more a GUI built-in behavior than it is an app-designed behavior, so it is able to add and display its menu options more independently of their actual behavior.