Both HP and PCP allow you to pay for your car in monthly payments over an agreed period, with a fixed rate of interest. The key difference is what happens at the end of each contract.
With a HP contract, you'll own the car after making the final payment.
At the end of a PCP contract, you can either hand the car back to the lender, part exchange it for a new one, or pay the final repayment (including any purchase fee) to keep the car. New finance agreements are subject to status and affordability checks. If you hand the car back at the end of a PCP agreement, there may be extra charges if you go over the agreed annual mileage or if the car has damage over fair wear and tear.