That's not it. The ZIP algorithm shows its strength when there is a lot of repeating byte strings. This is the case when compressing text files or documents, but not in images. With colors in the image changing even so slightly from pixel to pixel, such repeating strings are rare. ZIP can't find enough of them to get a significant decrease in size, so it's really not the best way to compress an image. (Neither is any other generic compression method, be it RAR, ARJ, GZIP, BZIP2, or 7Z).
A PNG image stores all the image data intact, as it uses a lossless compression algorithm. JPG on the other hand is only the approximation of the original image. Granted, the approximation is optimized so that the differences should be hard to notice to an eye, but they're there. Try to convert a screenshot to JPG and you'll see them plainly. The trick is, by using this lossy compression, JPG can achieve much better compression rates, at the cost of making it impossible to fully recreate the original image.
And this should work well enough. Just don't remove the source PNG images from your hard drive.
I'm not sure what your distribution workflow looks like, but I assume you have some automated procedure for creating a distributable package, something like a Makefile. If I were you, I would look into plugging some command line image conversion tools into this procedure. This way you could avoid exporting from Photoshop altogether, and let the command line tools to do the job. Send me a PM if you're interested and we can try to work it out.
