Pilots often blur "high-performance" and "complex," but the FAA defines them separately, and the same airplane can be one, the other, both, or neither.
A high-performance airplane is one with an engine of more than 200 horsepower. Note the word more — an airplane with exactly 200 hp is not high-performance. The classic example is the Cessna 182 (230 hp): high-performance, but with fixed gear and (in most models) a fixed-pitch-free constant-speed prop, it may or may not be complex.
A complex airplane has all three of the following:
All three must be present. A Mooney with retractable gear, flaps, and a constant-speed prop is complex. A Cessna 182RG (retract, flaps, CS prop, 235 hp) is both high-performance and complex.
The two endorsements are independent. A 180-hp Piper Arrow is complex but not high-performance. A fixed-gear Cessna 182 is high-performance but not complex. You may need one endorsement, the other, or both — and each is a separate logbook entry given after separate ground and flight training.
Getting these definitions exactly right is the single most-tested concept in this whole subject area.
Ask two questions of any airplane: Is the engine more than 200 hp? (high-performance) and Does it have all three of retractable gear, flaps, and a controllable-pitch prop? (complex). The answers are independent, so write them in two separate columns and never let one bleed into the other on a knowledge test.