See, the name 'piracy' makes it sound like you're stealing something, when in actuality, you bought and paid for it

Agreed. Moreover, the terms "piracy" and "copyright theft" make it sound like the original owner doesn't possess it any more. That's the reason why real theft is immoral, of course: not because the theif gains the item, but because the owner loses it. Such loss is simply not present in copyright violation cases; whether or not copyright violation is immoral, it can't sensibly be described as "theft".

Peter