As I checked out Gillette has these types of razors for men : Fusion Power, Fusion Mammal, Mach 3, Mach 3 Turbo, Mach 3 Sensitive, Vector 3, Vector Plus, Fusion Proglide, Presto disposable. And there may be more, which I never heard of.
These is the list of Indian brands available online for your razor quest.
Wells brands like Hary's are also available on Amazon.in, but they are too costly.