Stocks are ownership in a publicly owned company. If you own X number of shares you are entitled to that portion of the profits. Their value is set by the bid and ask price in the stock exchanges.
Commodities are products like wheat, corn, pork bellies, oil and gold. The actual products are not exchanged, they are traded as commodities futures contracts or options. Trading those contracts are used by producers to hedge the risks of price changes and weather events. For example a farmer may choose to sell his/her crop before it's planted at a known price rather than risk prices falling below the cost of production, causing a loss.