You've gotten the correct answer that scope grounds are generally shared, but rather than trust us, I recommend you try connecting a continuity tester, or DMM set to ohms, or similar device, between your two ground clips, while both probes are connected to the scope. You can easily prove to yourself whether or not your grounds are connected. (But if your experiment shows them to be isolated, be very suspicious. Double and triple check EVERYTHING.)
For isolated battery powered devices, that normally won't be an issue, but it can be a serious issue when trying to probe two signals in a single device, where the two signals are not isolated from one another.