“Person interested” is a person who is involved either directly or indirectly in the research of the same field of the invention whereas “any person” in general meaning is anyone who either belongs or doesn’t belong to the same field of Invention.
Eg: Invention to be patented is a New wind turbine. Here “person interested” means any person who is directly or indirectly involved in the research of turbines whereas “any person” means anyone for eg a salesperson of an automobile perhaps.