Since accounting is simply stated, the managing of finances, wouldn't accounting go under finance and vice versa?

Accounting and finance are somewhat related yet quite different. Accounting has (GAAP) General Accepted Accounting Principles) and corporations have to follow those to do their revenue, expense, cash accounting. Finance deals with numbers but can go into personal financial planning, corporate strategic plans where you do forecast and budgets but you are not as regulated on how you are reporting the numbers .

I was an accounting major, and I feel if you do that you can still have a finance understanding at the Corporate Level. However if you want to go and work for Investment banks, then finance would be a specialized subject that a lot of folks take when they specialize at the Master's level or do their MBA.

The simplest explanation I can give you is that Accounting deals with current and past transactions as they actually happened or are expected to happen. Finance is much broader and future-oriented, including all possible decisions and outcomes.

I studied Accounting in college, went on to get an MBA in Finance and Strategic Management, then became a licensed CPA. The two fields are very closely linked, and you have the ability to move between them during your career. At some point, you may decide to specialize, but experience in one is always relevant to the other.