"Stomach" is the correct spelling. An ache is a pain. A stomachache is a stomach pain. Most people with a stomachache just say they have a stomachache or their stomach hurts. Gastritis and gastric ulcer are medical terms. If a doctor has diagnosed that you have these conditions, then you should use these names. You can guess but you cannot self-diagnose that you have gastritis or an ulcer.

A stomach ache refers to any pain in the stomach, including diseases. It really describes just the pain. Gastritis and gastric ulcers are specific diseases.