“Is there one central pilot's license for all planes?”

Aircraft are certified in a category, class, and type. Categories include airplane, glider, lighter than air. Class includes single engine, multi-engine, land, sea. Type is a specific model such as Lear Jet 35, Boeing 777, etc. Licenses are for type of operation Private, Commercial, Airline Transport and for type/class- single engine/land, multiengine sea, etc. For jet and aircraft over 12.500 lbs, a type rating is needed.