No, the same driver is not used for both devices: the touchpad has its own whereas the USB mouse either has its own or uses the Windows default mouse driver.
As mentioned above, try disabling all of your Firefox add-ons, see if you can replicate the issue after doing so and then re-enable the add-ons, one by one, until you find the culprit. (If one of the add-ons is indeed the culprit.)
I run FF 3.6.x on Win 7 and do not have that problem.