The difference between 'Delete' and 'Destroy' in X window managers
If you use a certain sort of window manager (generally an old school one), you may have discovered that there are two operations the window manager supports to tell X applications to close themselves. Names for these operations vary, but I will go with 'Delete' and 'Destroy' for them because this is fvwm's terminology. Perhaps you've wondered why there are two ways to do this, or what the difference is. As you might guess, the answers are closely tied to each other.
The one way to describe the difference between the two operations
is who takes action. When your window manager performs a 'Delete'
operation, what it is really doing is sending a message to the
application behind the selected window saying 'please close yourself'
(specifically it is sending a
WM_DELETE_WINDOW message). This
message and the whole protocol around it is not built in to the X
server and the wire protocol; instead it is an additional system
added on top.
(Potentially confusingly, this 'please close your window' stuff is
also called a protocol. People who want to see the details can see
XSetWMProtocols() manpage and read up on client messages. See
eg this example, and also
On the other hand, the 'Destroy' operation talks directly to the X server to say either 'destroy this window' or more commonly 'terminate the connection of the client responsible for this window'. Unlike 'Delete', this requires no cooperation from the client and will work even if the client has hung or is deciding to ignore your request to close a window (perhaps the client believes it's just that special).
Generally there are big side effects of a 'Destroy'. Since most programs only create a single connection to the X server, having the server close this connection will close all of the program's windows and generally cause it to immediately exit. Even if only a single window is destroyed, this usually causes the program to get X errors and most programs exit the moment they get an X error, which of course closes all of the program's windows.
How programs react to being asked politely to close one of their windows varies, but usually if a program has multiple windows it won't exit entirely, just close the specific window you asked it to. Partly this is because the 'close window' button on the window frame is actually doing that 'Delete' operation, and very few people are happy if a program exits entirely just because you clicked the little X for one of its windows.
Because 'Delete' is a protocol that has to be handled by the client and some clients are just that old, there are or at least were a few core X clients that didn't support it. And if you write an X client from scratch using low-level libraries, you have to take explicit steps to support it and you may not have bothered.
(To be friendly, fvwm supports a 'Close' operation that internally checks to see whether a window supports 'Delete' and uses that if possible; for primitive clients, it falls back to 'Destroy'. I suspect that many window managers support this or just automatically do it, but I haven't looked into any to be sure.)
Sidebar: 'Delete' and unresponsive clients
It would be nice if your window manager could detect that it's trying to send a 'Delete' request to a client that theoretically supports it but isn't responding to it, and perhaps escalate to a Destroy operation. Unfortunately I don't know if the window manager gets enough information from the X server to establish that the client is unresponsive, as opposed to just not closing the window, and there are legitimate situations where the client may not close the window itself right away, or ever.
(Consider you trying to 'Delete' a window with unsaved work. The program involved probably wants to pop up a 'do you want to save this?' dialog, and if you then ignore the dialog everything will just sit there. And if you click on 'oops, cancel that' the whole situation will look much like the program is ignoring your 'Delete' request.)
I believe that some window managers do attempt to detect unresponsive clients, but at most they pop up a dialog offering you the option to force-close the window and/or client. Others, such as fvwm, just leave it entirely to you.