The difference is subtle, but potentially important. If the bank unfortunately gives money to someone else, that's their problem: I can say to the bank, I'm sorry you were the victim of fraud, but you still owe me my money. If I unfortunately "have my identity stolen", then that makes it seem like it's my problem -- the bank may say, we're sorry you "had your identity stolen" and thus lost your money, but that's not really our problem.
If I steal your ID card, then nothing really happens at all. I can spend years watching it, draw something on it, cut it in pieces, whatever.
The moment I start trying to impersonate you, then it becomes a problem for you.
If Bobby the metalhead downloads a copy of Enter the Sandman, then Metallica and brand doesn’t lose anything at all. If you were to make it industrial, then maybe we can talk about it.