As mentioned by others, the Capacitor on 1 phase Induction Motors is a Starting Device, not a Starting Aid - the Capacitor, in conjunction with the Auxillary Winding, creates an "Out Of Phase" magnetic field which reduces one side of the Stationary Field produced on the Main Winding - resulting in a "Somewhat" rotating magnetic field. The Auxillary Winding remains active until the Motor reaches >70% full speed.
The Capacitor Start method gives the Motor a higher Starting Torque - which will result in a higher starting amperage draw on loads such as compressor pumps.
The Cap Start/Run Motors will draw lower amperage under load, but not on starting [the run cap corrects the power factor and keeps the auxillary winding in the circuit, making the motor more like a Polyphase motor].
Also as mentioned, unloading the pump is very important! With high head pressure, the motor will draw high current for a long time until either it can move the pump piston[s] or the breaker trips [or the thermal unit[s] open].
Running a compressor with a pump sized 1.5 horse or more should be done at 240 VAC, so the current can be kept lower [starting and running].
Smaller compressors can be driven at 120 VAC, as long as they aren't being "choked" for current by long, small extension cords or branch circuits.
If you give a good sized pump a "Good" dedicated circuit, you should not have tripping problems. If the Motor's FLA [Full Load Amperage] is 12 amps @ 120 VAC and the pump matches the motor's horsepower, a 20 amp dedicated circuit should do just fine. Consider using #10 which will help out on any excessive I2R losses [voltage drop].
Also consider the "State Of health" that a circuit breaker might be in. Breakers which have been tripped a lot tend to either become "Loose" [trip to soon for their time/current charactersitics], or they become "No-Blow" [will not trip no matter how long an overcurrent flows through them!].
Excuse the techno mumbo jumbo! The others have posted better explanations. Only have one day to visit the forum and all this stuff is bottled up for a week!