How did columbus's plan for reaching asia differ from da gama's?

The main difference between the plans of Columbus and da Gama mainly differ in the way they tried to reach the continent, while Columbus was going for a much riskier option and wanted to reach Asian through unexplored ocean by going in a westward direction, da Gama was going for a safer option by traveling near the continental mainlands and was going south to go around Africa and than eastward towards the already known direction for Asia. This lead to different results, Columbus unintentionally managed to discover a whole new world for the Europeans, while da Gama managed to open up a route towards Asia that was clear of any charges or passing through the waters of some empire.