Your initial private-pilot certificate permits you to fly an ASEL (airplane, single-engine, land), only.
To expand your certification into flying other categories of aircraft, all you have to do is receive the appropriate training, fly with an instructor to verify your proficiency, and receive your instructor’s endorsement on your pilot certificate.
No new knowledge test or practical exam is required.
Most new pilots are happy to fly only the ASEL.
With additional training and an endorsement, you can add ASES (airplane, single engine, sea) to your certification.
And best of all, any ASEL can become an ASES with the addition of pontoon floats, which means you can turn your landlocked aircraft into a water bird, and fly away!
Or you can earn an airplane, multi-engine, land (AMEL) rating and fly twin-engine aircraft or move toward your ATP certificate.
Or you might want to try your hand at flying a powered parachute, a powered hang glider, or another category of aircraft without a fixed wing.
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The point is, once you have your private-pilot certificate you can use it to expand your knowledge, skills, and endorsements as far as you want — and can afford — to go!
"Man cannot discover new oceans unless he has the courage to lose sight of the shore."
-- Andre Gide