The difference:
Applications are launched, and they run until they are quit.
Windows are opened, and they are open until they are closed.
Applications are programs which enable you to use the computer to do your work.
Windows are (among the) Graphic User Interface elements which applications use to help you and the computer understand each other.
You will never hear me say, 'Close Archicad' or 'Quit that section window.' You shouldn't hear yourself say it either.
On the Mac, it is possible to have an application running, while all its windows are closed. The application itself does not have a window.
This means it is possible to have an application in the foreground with no evidence of its running expect the name atop the application menu, and its menus in the menu bar. Plus, you will probably see windows for other running apps. You may say, 'where is it?' It's right there. It doesn't have any windows open. To open a file, type Cmd+O or go to File | Open. To Quit, type Cmd+Q or go to [Application] | Quit.
Some apps (a few, really, and they're all tiny simple things) quit automatically upon closing their last or only window.
Running apps have a little black triangle next to their icon on the Dock. Click the icon to bring the app forward. (Note: some apps will open a blank document window when brought to the forgroung this way, assuming no other windows are open. Unfortunately, this includes Now Up-to-Date, which explains the blank calendar behavior.)
The confusion between Close and Quit, I believe, comes from using Microsoft Windows, the Official Operating System of the United States. On a PC, apps have a window of their own, even if no file is open. Closing this window quits the app. Only they call it exit. This is wrong, of course, because they are using the same interface element (the close box) to do two very different things. Only they don't think they're different. But they haven't really thought about it. Anyway everybody uses Windows.