If you press Cmd+Enter on iTerm while having the preference "Use native fullscreen windows" turned off, it goes into fullscreen but not the standard MacOS-way.
Is there a way of doing thisthe same in Terminal.app? I know I can use Ctrl+Cmd+F to enter a nativenative full screen. And I know I can maximize the window manually to eventually consume all of the screen, but in this case the title is still visible and there are some spaces around the window.