With leasing or PCP (Personal Contract Purchase rather than angel dust….i think) you pay for the car on a lesser amount than you would with HP as you are effectively paying off the depreciation plus some interest. This takes into consideration a mileage allowance.
Your repayment can include a set amount upfront e.g. 3+36 or it can be without a deposit. At the end of your payment plan you then have 3 options. Pay the final installment which is the residual value of the car, hand the car back or trade the car in on another finance agreement.
If you trade in it doesn’t have to be with same dealer as they will give you a trade in value of your car which will hopefully cover your final payment. If you trade in with the same dealer they are likely to wave any excess mileage penalty.
Its a good hassle free way of buying (well leasing really) a car but doesn’t make sense if you are putting a large deposit down.