I think you have it sorted out properly: JPG is a good file type for photographs and other 100% opaque images with a lot of tonal variation. GIF is a smaller file format for images with flat color (cartoon or illustration style) and for images where you need a transparent area.
PNG is a lesser known file format with native support for alpha transparency, but currently enjoys only partial browser support for it's more advanced features. Check here [webmasterworld.com] for links to more info on PNG... It may be what you're thinking of.