Welcome! I see you're new here! This is the internet, everyone is an expert on everything. Master and Chief internet editor.

Newton's laws of motion? Inertia? Any of that ring a bell? If you want to be absolutely technical in the purest sense of the word, yes, both objects would be moving. However, if there is any disparity in mass, the movement of the more massive object is less than that of the less massive object. If the difference is large, the movement of the object with greater mass will be imperceptible. Never claimed to be an expert. I just took physics in high school.