that may be a bit simplistic FD.
there are 2 basic types of props - fixed pitch, and adjustable pitch.
fixed pitch are just that - optimised for a particular phase of flight - a fine pitch (meaning the average pitch of the blade, or its Experimental Mean Pitch) is best for climbing, short field take off, higher static RPM, and slower flight. a coarse EPM gives good cruise speed, lower static RPM, longer take off (slower to accelerate). Fixed pitch props are light, easy to maintain, and easy to manage - engine RPM = prop RPM (yes even if the prop is geared down like in a rotax).
a CSU (constant speed unit) receives an input from the pilot via the prop lever, which sets a speeder spring weight on a set of flyweights. through the magic of oil, gravity and rotational velocity, the prop will maintain the RPM set by the pilot - it will fine off in a climb (lower speed) and coarsen in a descent/cruise (higher speed), giving the advantages of multiple/indefinite variations of pitch for the airspeed required. CSU's tend to be on light twins, or higher performance singles, and are on all turboprop aircraft.
some props are essentially fixed pitch, but can be adjusted manually in flight or on the ground - these tend to be fitted to performance light/microlight aircraft. they don't have the complexity/weight of the CSU, but have some of the advantages - pitch can be set depending on the mission.