What is one main similarly between the digestive system and the respiratory system?

They are both involuntary systems. Meaning the initial part of the process may be controlled like eating and chewing or holding your breath, but the rest of it is something that just happens and you don't have to think about it. For the most part you don't even think about the breathing. They both obviously keep you alive, but it's because your body takes aspects of each to do so. Removing oxygen from the air and putting it into the blood stream and removing nutrients from food to power cells. Thirdly, they both take something in, use it, and remove the waste.