The main difference between buying a car and leasing a car is that in the former case you own a car eventually, while in the latter you are only renting it from someone else.
If you consider one of these options, then chances are you do not have enough budget to purchase a vehicle right away, and hence you will be applying for a car loan. With bad credit, your interest rate will be significantly higher than usual, plus you will also be paying for the repairs and monthly maintenance of the car; keep it in mind when calculating your budget. However, even with bad credit you still have a chance of buying a car via getting a loan. With car leasing the case is different.
Car leasing contracts last for about two to three years, and they are primarily granted to people with good credit score. With a bad credit score, it will be hard to find a company that will lease a car for you. This is easily justifiable because whenever you get a car loan, the actual vehicle is used as collateral which can be taken from you to cover the missing payments. When you sign up for a car lease, you do not own the vehicle, so whenever you miss a payment, the leasing company cannot make up for them with a car since they already own it. While leasing a car to a client with bad credit is a rare move for businesses, even if they do, you will be facing significantly higher monthly payments as well as additional restrictions in terms of maintenance, mileage, and wear and tear.