maybe you didn't quit the app b4 ? by clicking the red button in the top left, you only closed the one window of that app, to quit you need to press cmd+q
so if this is the case, just press cmd+n and you will get a new window of that app (this shortcut probably doesn't work everywhere though, there will be similar in every app) or just quit the program and run it again
you can tell easily an app is running if it has a blue circle below it's icon in the dock (it will also be visible in Activity Monitor of course, or if you pres cmd+tab you will cycle through running apps, again cycle through apps that are on, not necessarily have an open window)
I hope it's not too confusing