Question: what is de Quervain's tenosynovitis really?

Tenosynovaginitis. Yes, that word. It's a problem of the tendon, it's lining, and the sheath of one of the thumb tendons. They get irritated and enflamed. It's quite painful. They become thick and hard so the tendon can't slide normally. This just makes things worse. Early on, the first month or two, a cortisone shot and a brace can be effective treatment. Later, it requires surgery.
Inflammation. This is an irritation or inflammation of the tendons on the thumb side of the wrist. Mainly causes pain on moving the wrist especially toward the little finger side. It is treated with anti-inflammatories like advil (ibuprofen) and rest. Sometimes splints are used, occasionally an injection of steroid is used and may require surgery if none of these releave the symptoms.