Finance is a noun …

Financial industry refers to an industry (just like manufacturing), including banking, insurance, securities, futures and so on …

Financial business refers to related businesses in the financial industry, such as bank transfer, fund subscription, bond/creditor's rights transfer, asset custody, insurance purchase and futures subscription.

Financial service industry is related service industries and businesses around finance, such as financial information consulting companies, evaluation companies, brokerage companies, etc.

It may not be comprehensive, I hope I can help you … thank you.