system preferences -> dock -> checkbox for "Double-click a window's title bar to: " an the options are zoom or minimize.

If its set to zoom, the window will grow taller, doesnt seem to get any wider for me, but it does get larger overall.

I've never figured out what the green button does besides make the window larger and randomly sized. I always figured there was something that the size was tied to but never invested the time in figuring it out. I use SizeUp and never click on any of the buttons now anyway. I do miss Windows for this functionality.

Most programs I use, the green button causes the window to go full screen and switch to another desktop. But double clicking the title bar in Safari, for example, sets it to what seems to be an arbitrary width and maximized from top to bottom of the screen. I don't know how to get it to fill the entire screen without switching to another desktop.

The intent is to size the window to fit the content. For example, if you're viewing an image, then the window's size would be set to the image's size (or to the screen size, if the image is bigger than the screen).

For something like Safari, there often isn't a single sensible content size, so it ends up just trying something reasonable for the width.

It does in el capitan.