Font Differences

I recently wrote a Java application for the PC (NT) and tried to port the code to a UNIX environment. The code worked fairly well except that the representation of the fonts on the platforms was so different that I couldn't predict what size the original frame was going to be. I check to see what fonts are being displayed on both platforms, and both verify a sanserif 12 point font. Both displays are 1024 x 768 in resolution but the UNIX font is considerably larger (in pixels) than the PC. Why is this, and What solution is there so that the application is truly "portable".