Hi, in case of Pune/Maharsahtra, there is usually not much difference between the two. A rent agreement is for a 11 month period, after which it must be renewed. A lease agreement is more long-term ( 3 years and upwards). But yes, you can make a 3 year rent agreement too and register it accordingly.
Usually however, rent agreement is used in connection with residential properties and lease agreement in connection with commercial properties.