Are back and shoulder pain always caused by the same thing or can they not be related?

May not be related. Shoulder and neck pain may or may not be related. If it is related it is probably because of a pinched nerve in the neck (we call that cervical radiculopathy) that is referring pain to the shoulder. However a person can definitely have two things separately going on but usually it does not start at the same time. Meaning one usually started before the other.