A DRIP is a dividend reinvestment plan that a company sponsors for existing shareholders. You must be a shareholder in order to participate in a company's DRIP, and any dividends paid by the company will automatically be reinvested in additional shares of stock in your account.
A DSP is a direct stock purchase plan. Companies that have DSPs allow anyone to buy shares from the company directly. Following that initial purchase, the plan operates just like any dividend reinvestment plan (Some companies that don't pay dividends do have direct stock purchase plans, though.)
The difference really comes down to how the initial shares are acquired, either directly from the company or from another source.