What is the relationship of CloseWindow and WM_CLOSE

CloseWindow is an unusually poorly named winapi function. It doesn't actually close a window, it just minimizes it. What you possibly meant was DestroyWindow().

WM_CLOSE is normally a message that's generated by default window procedure, in response to the user pressing Alt+F4 or clicking the window's close button. The underlying message is WM_SYSCOMMAND, SC_CLOSE. It can be generated in code as well, like a Window + Close menu item.

You can listen for WM_CLOSE in your window procedure or the MFC message map. The user will expect the window to be closed. So you normally call DestroyWindow(). You don't have to, you might display a message box for example and ask the user if data should be saved. And if he clicks No then you don't call DestroyWindow().

CloseWindow and WM_CLOSE are completely unrelated. The CloseWindow function is badly named. Its inverse function, OpenWindow is similarly badly named given that it restores windows.

I suspect these names dates back a very long way indeed, probably to Windows version 1 or 2. I'm speculating that what we now call minimize and restore were, back then, called close and open.

The usual way to minimize or restore a window is to call ShowWindow passing SW_MINIMIZE or SW_RESTORE.

I suggest that you forget all about CloseWindow and OpenWindow.