Accounting is a record-keeping function, focused on the day-to-day flow of assets within and without an entity. The goals are to have complete and accurate reporting and full compliance with laws.
Finance is the control, custody, management, and planning of assets.
@RedDeerGuy1, your assertion is somewhat correct. Accounting looks back to past transactions and knows current position; finance is more concerned with future growth. But, each discipline is broader than just that.
BTW, the two functions should never be mixed. Unfortunately, many entities make this mistake – believe that anything with a dollar sign should be handled by the same person. Consider an employee who has check-signing authority, can transfer money in-and-out of accounts, reconciles the bank statements, and keeps the books. This is a person who can do anything and cover his/her tracks with impunity.