My 8.5 month old woke up this morning with a runny nose and he's drooling. Are these symptoms of teething or does he have a cold?

Yes and no. The drooling may be related to the teething, but the runny nose is likely due to another condition such as a cold.
Either or both. Hard to tell without seeing but either way if there is no fever and he is otherwise doing okay, you would treat it the same way. Salt water nose drops and suction the nose when it is stopped up. If there are more symptoms particularly fussiness see your doctor.