The pitch isn't necessarily going to be the same. Remember that if a piece of hardware is only an implementation of a concept. In this case, the sound card may have its own set of instruments, the output of which ultimately depends upon the frequency of the signal from the hardware. We could even expect there to be some variance in sound between two separate cards - if it were an older soundcard, for example, it would be reasonable to expect that it has a lower frequency depth resolution - or a lower number of different possible output frequencies.

In reality, it's just that different hardware implementations are not necessarily identical. And that's assuming that playback isn't affected at all by - as Samuraid said - the software renderer.