Vince,
Easiest way to use it on both is to format it for PC. Backup your music using a utility like podutil (it takes the music back off your ipod), reformat it for PC, and readd your music to it. It seems PC's don't like Mac formatted ipods, but it works w/o issues the other way.
Also, it won't show the charging icon when connected to a computer, only when you have it plugged in to the wall. It will show the sync display, but will be charging as well.