Maximize windows does not fully max the window

The green button goes full screen, as you said. Option clicking the green button sizes the window to show the whole document. In the Mac world, there is no reason to arbitrarily make a window as large as the entire screen. That’s something that Windows users desire. All you can do is manually size the window by dragging the edges.

You might find this articles useful:
http://www.macyourself.com/2011/02/06/why-doesnt-mac-os-xs-green-zoom-button-maximize-windows/

 

If you want full screen, just press the green button (not Option-green)
That takes your pdf file to full screen, but not necessarily what you want

If you want the window, with the PDF document, to fill the screen, but not actually go Full Screen, Option click usually fills the desktop vertically, and horizontally to provide a space for the whole document. If that is NOT the full width of the screen for the full size, then the window only expands to the space needed. It will often be different for every PDF that you try. Some will go full width, and others will remain in a narrow area, if that's all there is to the document.

Macs don't do screen-wide windows by default, unless the document does. It's one of those items that differentiates the macOS from other "windows" systems. Keep in mind that some individual apps will do other adjustments to the window that displays the app, and may be near full screen in normal circumstances - single-window apps such as iTunes does that.

Option-Green button, than adjust the window manually to your liking.

 

...or what they're used to. Although I used Windows at work before buying my first home computer (a Mac) I prefer to be able to click outside an app's window to the Desktop. At work, it's sometimes a battle with Windows to prevent apps from going full screen, but I invest the effort to do so.

Bottom line, on the Mac, it's not going to act like it's Windows. You can't make many (or any?) windows cover every pixel of your screen. It may take some adjusting of your personal preferences, but you just have to adapt to this as your Mac is in control of the situation in this case, not you.