Student or Learner
Is there any difference between "She rented a car for a day" and "she rented a car by the day"?
'by the day' :
Consider a car rental company that rents cars only 'by the week'. That means that whether I want the car for one day, four days, or the whole week, our agreement is that I must pay for a whole week.
The same is true if a holiday house is rented by the month. If I have to cut my holiday short before the month is up, I still have to pay the full month's letting fee.
So - 'by the day' means that my contract is for each 24 hour period. I can rent a car for a day at 10 a.m. Monday; and if I wish, ring Avis before the car is due back 10.a.m. Tuesday, and arrange to borrow it for another day. OTHERWISE, they expect the car to be returned after one day; but if that model car (the only one Avis has of that type) is not pre-booked by someone else, then I can keep extending from day to day if I wish.