Yep, in PSC motors the capacitor is energized full-time while the motor is running (both windings also energized). PSC motors utilize 3 power leads (not counting the case/earth ground) and are often impedance protected by design.
Another PSC characteristic is that a multi-speed PSC motor doesn't require extra power leads, as changing the capacitor value can change the speeds.. a two-section capacitor with 2uF and 4uf can be switched to provide 3 speeds by using 2, or 4, or both combined in parallel for 6uF, for example.
The capacitor value for PSC motors is a low value up to around 20uF or sometimes slightly higher.
In split-phase capacitor start motors, the capacitor is only energized momentarily during startup.
The split-phase capacitor start/CSIR motor utilizes a centrifugal switch to attain it's run speed, and has only 2 power leads (not counting the case/earth ground) and the same applies whether the motor is split-phase without a start cap, or split-phase capacitor start and capacitor run type.
Start capacitor values for SPCS motors is generally high with a value of approximately 500uF per horsepower (fractional HP motor start caps typically about 100uF).
So there are several differences that make identification of the motor type fairly easy, hence the capacitor type.
Knowing the actual use/type of cap may not be of much use when inquiring at a parts counter though.. many sellers of motor caps mis-state the correct terms.