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TL;DR: Trafalgar Law is a real pirate. Stop thinking he won't, or shouldn't do pirate things. All things considered, the Strawhats really do not qualify to be called pirates.
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They do not follow the law. They are criminals.. which is not to say that they are the 'bad guys', but in the eyes of the World Government they are enemies.
The OP world consists primarily of ocean and (small) islands, not continents like ours. Thus most of the more powerful characters in that world do not primarily stay in a single place because each place is so limited in scope (think a Caribbean island).. and so as outlaws become more powerful they will inevitably seek their fortunes by boat. An outlaw on the ocean can be called a pirate.
If Luffy and Co paid any respect to WG laws, they would indeed be bounty hunters.
You are right though that before the Arabasta arc, their actions were that of mere adventurers. Their classification as pirates was the result of two factors: 1) the fact that they called themselves pirates and they had a jolly roger and 2) the actions of the corrupt Marine Nezumi.