stevenr868's answer is correct. "pain" and "ache" are also used to refer to things besides physical pain and discomfort. "It pains me to inform you that you failed the test." This means that "I'm sorry to inform you..." "pains" can also be used to describe something involving great care and effort - "He took great pains to set up the camera." "ache" is used to describe some longing or constant sorrow. "She's been away for weeks now and my heart aches for her."

a pain is a more general term that can relate to any discomfort. an ache is more like a continuing, often throbbing pain