If you are taking a property on lease you must pay one time payment which will be a large amount but according to rent it is some what low the reason is that rent should be paid on the given timings in some installments and lease can be taken on one time payment which will be beneficial than rent. by taking on lease you may get discount upto 5-10%.
This is a little confusing the way it is written, but I think that I understand what you are saying. Where I live, if you want to rent you have to sign a lease, and that is for like 6 months or a year. You then pay a deposit for your house, and first and last months rent. Even though you have a lease on a property you will still need to pay rent every month. At least that's what I have experienced.
Does this depend entirely on the landlord to come up with such terms and conditions or its the governing law in your country that puts in force such laws and regulations? Just curious that's all.