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.
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.
(Mitchell & Webb Sound - Identity Theft)
This should be called "identity validation failure".
When scammers impersonate a company to steal your money it's no longer called identity theft.