Both destinations are served by Seychelles Int'l (SEZ). Since there's no flight route between them, the best way to travel is by road.
Mahe Island
Fly to Seychelles Int'l (SEZ), then travel by road to Mahe Island. Taxis, buses, and private cabs are available from the airport.
Seychelles
Fly to Mahe Island (SEZ), then travel by road to Seychelles. Local transport options include taxis, auto-rickshaws, and state buses.