If you're interested in working for taxi services, then you've unduly wondered what kind of arrangements these companies work out with their drivers in respect of the vehicles that the drivers use on a day to day basis. The truth is that the arrangement differs from company to company. Some companies lease their vehicles to their drivers, others have them buy the cars, and some allow both.
The vast majority of companies in this business are going to ask their drivers to lease a cab from their organization. This has simply become the standard accepted model of how these types of companies are run. The only companies which would require that all drivers buy a cab must be very, very small, with a dedicated contingent of drivers. This would be more common in a company that drive luxury shuttle cars instead. The reason is that it is simply too big a commitment to require someone to buy a cab just to work as a driver, especially when they do not really know if that is a job they are going to enjoy doing or not for any amount of time.
This is why most companies lease cars instead. Actually, they lease their drivers a complete package that includes everything that they're going to need to run their taxi successfully. This means that they'll get the car, but also a meter, a radio, and payment processing equipment. That way they are ready to begin with their lease package as soon as they complete their training.
There are some large companies that lease most of their cabs but still have a purchase option in place as well. That is sort of a courtesy that they extend to dedicated drivers that have been working in the industry long term. By allowing them to buy their vehicles they are allowing them to invest in their business, and hopefully to build a more profitable endavor than just leasing a cab allows for.
The exact rules for leasing or buying cabs are going to be different between every cab company. If you've never driven a cab before because and are interested in getting into the industry, the recommendation is to always lease before you buy. Buying a vehicle is a significant financial commitment, and a cab can be hard to sell quickly if you decide the job is not for you. Leasing gives you a window to test the job, and if allowed you can purchase later.