This is a topic that has been bugging me recently.
When creating a game in a JFrame, and you want to add the graphics to a JPanel with the paintComponent()
"Abandon all hope, ye who enter [through Swing to create games]!"
To answer your question, JPanels are just a surface to draw on, like a chalkboard, or a piece of paper. They have nothing to do with stages, or anything else other than being a thing you can draw on, and a container for other sub-components.
To address the game-specific question, I'd recommend you don't waste your time using Swing components to build a game interface. While it's possible, you're going to run into a bunch of performance problems that will just eat up your time. Based on your question you're already thinking about low-level stuff like Timers to schedule things, and overriding the paintComponent()
method - a very common mistake, and a road that many a failed project spend time on just to find out it's not the best way.
If your question were literally a path in a forest that you could see, you would notice these things:
Instead, use something like Slick2D (for 2D games), or jMonkeyEngine for 3D shtuff. These libraries are designed specifically for building games, and are going to save you from having to reinvent the proverbial wheel, just to get your game up and going. They also have their own communities that can help you with library-specific issues.
On top of that, they have already solved some of the trickiest cross-platform issues, like dealing with various versions of OpenGL, and other technical details that I'll bet you don't really care about when at the end of the day, what you really want is, "Hey, just give me an [arbitrary resolution], graphics-accelerated surface to draw on, and don't make it complicated!"