To take it to an extreme, it's like saying you murdered someone when you ran a red light and hit their car. Yes, they died, but you're only really guilty of involuntary manslaughter. Manslaughter gets you 5-10 years, murder gets you life. Two sides of the same coin, maybe, but wildly differing laws, punishment, and intent.

Stealing and pirating are both taking something that is not rightfully yours, but they are barely in the same category of crime.

Pirating is sharing something not rightfully yours, not taking. Making and circulating copies is illegal, not receiving copies.