Answer:
Yes and no. A savings account if not a bank account would be an investment account. If a savings account is used for operational use on a day to day basis then it would be seen as a bank account. If it is used as an investment account then it will not be classified as a bank account.
Yes, a savings account and a bank account are the same thing!
Recent law changes have made it that the Savings Account should not be used as a regular every day to day account. There are penalties that accrue after using it 3 days in a period (about 1 month). Most banks will at that point either shut down your savings account or convert it to a checking.