Both destinations are served by Kolkata (CCU). Since there's no flight route between them, the best way to travel is by road.
Calcutta
Fly to Kolkata (CCU), then travel by road to Calcutta. Taxis, buses, and private cabs are available from the airport.
Kolkata
Fly to Netaji Subhash Chandra Bose International Airport (CCU), then travel by road to Kolkata. Local transport options include taxis, auto-rickshaws, and state buses.