I would maybe reframe it as fraud being a natural downstream effect of identity theft. I don't need to steal anyone's identity to forge a check but that's also categorized as fraud.

Identity theft also paints a clearer picture of what is required to remedy the situation. If your details have been pwnd hard enough, you might need to get new government documents entirely in order to protect yourself long term.

If a contractor takes my money to install a pool and then disappears, I don't need to reset my entire financial identity. I think it's worth having a separate idea to describe the situation as a whole and not just the specific vector in which a crime might have been committed.