While the two certainly do not mean the same thing the only thing I can put forward is a simple thought.
If something exists that doesn't belong to you and you take it without paying or exchanging for it (or permission from the owner) then it is stealing. Now that goes for intellectual property as well as physical.
That said, torrenting and pirating are still different things. I also don't totally believe that it's immoral to download some songs off the internet. The reason I don't do it is because I'm that guy that always gets caught with that crap.
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