Understanding the behaviour of Emacs and Emacs Client

[Pankaj Jangid]

I am on version 29 (Git-master). And I "make install" into $HOME/.local
on a Debian (stable) system. I am using Gnome.

Now I have two application icons - Emacs and Emacs (Client). I want to
understand the behaviour of these two links. Following is what is
happening on my system and I want to know if that is the desired
behaviour:

1. When I launch Emacs by clicking "Emacs" icon from apps. Emacs
   launches as usual and shows "Emacs (Client)" near the Activities menu
   in Gnome shell. And when I exit Emacs, C-x C-c, it is perfectly
   shutdown.

2. When I launch Emacs by clicking "Emacs (Client)" icon from
   apps. Emacs launches as expected. And shows "Emacs (Client)" near the
   Activities menu. But when I want to exit this instance of Emacs, I
   press C-x C-c and the frame is gone. But there is still an Emacs
   process running.

I want to know if this is the desired behaviour of Emacs. And if Yes
then what is the official way to terminate the residual Emacs process in
case (2) above?

~Regards Pankaj