Very interesting comment. For me the line is profiting from the copied content/software. I am opposed to people selling pirated movies on the streets and not so to people downloading and watching them in their homes.
The name would be covered under trademark law, and the website/graphics copying could be considered plagiarism if you are attempting to pass them off as your own.
On the other hand, someone that copies a movie is neither:
1) Claiming to be the movie studio that produced and/or distributed the movie.
2) Claiming that they were the producer/creator of the movie.
Comparing the two situations doesn't work because the only common factors are that copying happened and that they're both related to the nebulous term 'IP.'