macOS: Is there a way to maximize a window but does not go full-screen?

Move the cursor to any one of the four corners of the Window. When the cursor icon changes to a diagonal bi-directional arrow, press and hold the Option key and double click.

This would maximize the window to occupy the entire screen without it entering into full-screen mode.

If you want this consistently, you will need to install a third party utility, like Rectangle, Magnet, Moom or several others.

In some cases you can hold Shift ⇧⃣ while clicking the green stoplight button to have a "cover the whole screen, but don't go into full screen mode" behavior, but this depends on the app.

The reason for this is that historically, macOS had no concept of windows covering the whole screen:

• In classic MacOS the widget would make the window change to a size that is best fitting the content of the window. This could enlarge or shrink the window. You can check it out using an online emulation of System 6.

• MacOS X changed the location and the appearance of the window widgets , but the green stoplight had the same behavior up until OS X 10.9 Mountain Lion.

• MacOS X 10.7 Lion added a zoom widget at the right side of the window that would switch the window into full screen mode and back.

• OS X 10.10 Yosemite replaced the default behavior of the green stoplight with "full screen". The previous "best fitting size" behavior was moved to two places:

  1. You could press Option ⌥⃣ while clicking on the green stoplight
  2. You could double click the window title

This is the behavior up until macOS 10.16 Catalina, so this is what you are experiencing.