The bond market is where investors go to trade (buy and sell) debt securities, prominently bonds. The stock market is a place where investors go to trade (buy and sell) equity securities like common stocks and derivatives (options, futures etc). The differences in the bond and stock market lie in the manner in which the different products are sold and the risk involved in dealing with both markets.
One major difference between both markets is that the stock market has central places or exchanges (stock exchanges) where stocks are bought and sold. However, the bond market does not have a central trading place for bonds; rather bonds are sold mainly over-the-counter (OTC). The other difference between the stock and bond market is the risk involved in investing in both. Investing in bond market is usually less risky than investing in a stock market because the bond market is not as volatile as the stock market is.