'Happiness' is a vague term which refers to various prominent sensations and to a more general state, as vague and abstract as CEV (e.g. "Life, Liberty, and the pursuit of Happiness"). 'Headache', on the other hand, primarily refers to the sensation.

If you take an aspirin for a headache, your head muscles don't stop clenching (or whatever else the cause is); it just feels like it for a while. A better pill would stop the clenching, and a better treatment still would make you aware of the physiological cause of the clenching and allow you to change it to your liking.

A: I don't believe in love. It's just a bunch of chemical reactions. B: [kicks A in the balls] A: WHYYY??! B: I don't believe in pain. It's just a chemical reaction.

-- SMBC on explaining vs. explaining away.