Option A can likely be structured as a store incentive whose total dollar cost to Walmart is below that of an hourly worker.
Option B would likely be an employee requiring additional taxes to be paid and benefits to be supplied.
This is not a comprehensive argument.
I think Walmart wants to (or they should) have a little more control to ensure that the driver doesn't steal my order. An employee gets a background check...
I think the difference would be that you were probably going to come to the store anyway for whatever reason.
So option B is really, "A driver starts at Walmart, picks up three people's shopping, delivers it all, returns to Walmart. You also drive to Walmart, pick up your shopping, and drive home."
Option A: You drive to Walmart, pick up your shopping and three other people's, you drive home via three other homes.
Option B: A driver starts at Walmart, picks up four people's shopping including yours, delivers it all, and returns to Walmart.
Seems to me the number of person-hours and distance driven is identical in both cases?