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Classically, some therapies for headaches are thought to be effective in only certain classifications of headaches, such as triptans in migraines, or oxygen in cluster headaches. This is not necessarily true.
Triptans have been successfully used in cluster headaches, as found in the 2013 Cochrane review.1
More recently, "high-flow" oxygen (referring to 12 L/min of oxygen, delivered through a facemask) has been studied in migraine headaches, with promising results. When compared with placebo (air), oxygen used for 15 minutes was more effective in pain relief and improving visual symptom, with no significant adverse events. 2
References
1. Law S, Derry S, Moore RA. Triptans for acute cluster headache. Cochrane Database Syst Rev. 2013 Jul 17;7
2. Singhal AB, Maas MB, Goldstein JN, et al. High-flow oxygen therapy for treatment of acute migraine: A randomized crossover trial. Cephalalgia. 2016 May 20.