You hear the words "economics" and "finance" often used interchangeably. There are, in fact, important differences between the two.
Economics is the study of markets. Markets are places where participants come and trade goods and services.
Finance, on the other hand, is the study of the financial market. The financial market is a market where borrowers and lenders meet. Borrowers are people who need money straight away, e.g. to start their own business. They do they by taking out loans or raising money by issuing shares. When borrowers take out loans or issue shares, there must be lenders or stockholders on the other side of the trade. These people lend money or buy stock. Finance is simply a study of the market where the patient (lenders) and the impatient (borrowers) meet.
It is clear from this that finance then is a branch of economics just like neuroscience is a branch of medicine. Buying and selling stocks or bonds is a finance issue whereas buying and selling oil is an economic issue. Economics is broader than finance because economics studies all markets whereas finance only studies financial markets.
All finance is economics but not all economics is finance.