How to have different window tiling options?

You are referring to tiling. Tiling options in default Ubuntu are very limited. You can only tile left and right half of the screen.

With an extension, WinTile: Windows 10 window tiling for GNOME by Fmstrat, you can expand tiling capabilities. The extension can also be set to work with three (and four) vertical colums, so you could tile 1/3 of the screen.

To allow for 2/3 tiling, you must change some options in the Wintile extension:

• Set "Number of columns" to 3
• Uncheck "Use true maximizing of windows"
• Uncheck "Enable preview and snapping when dragging windows

With these settings, a layout like

1st window: 1/3 of screen 2nd window: 2/3 of screen"

is actually possible.

• Hit Super+Left to tile the first window 1/3 of the screen
• Select the second window, then maximize with Super+Up then hit Super+Right to tile it in the right 2/3.