Since that feature was introduced I think I only ever used it by mistake. I think it would make a lot more sense if pressing alt would allow for fullscreen and normal click would be maximize.
What I'm describing as the "opt" behavior is the classic maximizing behavior on both Mac and Windows (except Windows doesn't have a top bar).
If you don't hide the dock/start bar it maxes to its limit, if you hide it goes to the bottom. Maybe it was unclear when I didn't mention it'll max side to side too if the bar is on the bottom. If bar is on the side it'll leave a gutter on the side.
TL;DR it's a normal maximize--doesn't cover the doc or menu bar and you can float windows in front of it since it's not full screen mode.
I tested it on a few apps before I posted (and after you replied) and it looks app-specific.
Finder actually fills the screen (the Apple app I did originally test since it used to represent reference windowing behavior) but only in list mode, which happened to be my default. In icon mode it does the old school top-to-bottom thing, as I found out after the replies.
But Chrome fills the screen, OmniFocus fills, Keyboard Maestro's editor fills, Firefox fills, etc. I think a lot of third party apps will fill the screen since it seems to come down to whether the dev gives it a different aspect ratio than native to "show all content." Most stuff seems not to do so anymore, presumably because that behavior is weird.
But to your point, apparently Safari was a huge oversight on my part and it's definitely not as consistent as I thought it was. Sorry if I got hopes up.
That said, to the extent an app will do that at all, opt-click-max or title bar double-click is the way to do it. Otherwise you're stuck with one of the screen snap apps that can also redefine the buttons for you.
Spectacle is no longer maintained (it may matter with Big Sur release). Rectangle is based on Spectacle and is actively developed: https://github.com/rxhanson/Rectangle
The top menu bar is also hidden when apps go full screen.
I think the only alternative is to hold down option key when expanding the window.