What is the difference between a controllable-pitch and a fixed-pitch propeller?

The practical difference between fixed and controllable pitch shows up most clearly in how the ship manoeuvres and how the engine is operated, not just in the mechanics of the propeller itself.

With a fixed-pitch propeller, thrust is controlled purely by shaft speed, so going from full ahead to stop to full astern on a large slow-speed diesel means actually stopping the engine, reversing its timing, and restarting it turning the other way, a sequence that takes real time and cannot be rushed without risking the engine, which is why large FPP ships plan manoeuvres well ahead and bridge teams treat astern propulsion as something that takes a definite number of seconds to become available, not instantaneous. The simplicity of an FPP, a solid casting with no internal mechanism and no hub seals to maintain, means fewer things to go wrong and slightly better propulsive efficiency at the one loading condition it is designed for, which suits ships that spend most of their life at a steady service speed on long ocean passages, such as bulk carriers and tankers.

A controllable-pitch propeller keeps the shaft, and often the engine, turning at a constant speed while an internal hydraulic mechanism, oil delivered through the hollow shaft to a servo piston in the hub, rotates each blade about its own root axis to change the pitch angle. Moving the pitch from full ahead through zero to full astern varies thrust smoothly without ever stopping or reversing the engine, giving much faster, finer control, exactly what a ferry doing frequent, tight harbour manoeuvres, a tug working close alongside another vessel, or an offshore vessel doing precise station-keeping needs. Running the engine at constant speed also makes a CPP the natural partner for a shaft generator, since constant shaft speed keeps the generated frequency steady without extra power electronics.

The price of that flexibility is complexity: a CPP hub contains a hydraulic mechanism operating inside a rotating, submerged assembly, sealed against seawater ingress, and a fault in the hydraulic system, low pressure, a leaking hub seal letting water into the oil, or a jammed blade, can leave the propeller stuck at an unwanted pitch, sometimes ahead when the ship needs to stop. CPP installations are therefore maintained on a stricter regime, checking hydraulic oil condition and water content, hub seal integrity, and the pitch feedback system, and a CPP is somewhat less efficient than an optimally matched FPP at any single fixed operating point, since its blade sections are a compromise across the whole pitch range rather than optimised for one.