Resolution vs. compression

[Livingston]

I just bought a G6. What a toy!!!

I am somewhat familiar with digital photography and image processing, but mostly the basics. The G6 has settings (still) for both resolution and compression. I think I understand resolution but the compression stuff confuses me a little.

I think I understand the resolution settings. My assumption is that this setting adjusts the pixel density on the image being stored on the card. I hesitate to use terms like "pixels per inch" but that's as close an analogy I can come up with. My assumption is that the processor in the camera is doing something like taking areas of the image and resolving them to a greater or small number of pixels based on the resolution setting. In a sense there is some compression being done based on this setting.

Now, looking at the compression settings (3 of them) I'm assuming that further compression is being done to the resultant data but that's where I lose it. Since all images are stored as JPEG (unless I use RAW) does the compression setting coorespond to different JPEG compression algorithms? Or is there something else going on here?

Also, does the processor first deal with resolution and then with compression?

Thanks