Step motors and servo motors service similar applications, ones where precise positioning and speed are required.
The biggest difference is steppers are operated "open loop". This means there is no feedback required from the motor. You send a step pulse to the drive and take on faith it will be executed. Seems like a problem but it's not.
If you have a quartz watch with hour and minute hands, then you have a step motor on your wrist. The electronics generates 1 step pulse per second, driving a 60 step per revolution motor which turns at 1 RPM. It keeps nearly perfect time. Any errors are due entirely to the electronics timing accuracy (quartz crystal oscillator).
With apologies to David Letterman, here's some "Top 10" lists I came
up with for choosing between steppers and brush DC servos. Others can
add more, I'm sure.
Top Ten Stepper Advantages:
1) Stable. Can drive a wide range of frictional and inertial loads.
2) Needs no feedback. The motor is also the position transducer.
3) Inexpensive relative to other motion control systems.
4) Standardized frame size and performance.
5) Plug and play. Easy to setup and use.
6) Safe. If anything breaks, the motor stops.
7) Long life. Bearings are the only wear-out mechanism.
8) Excellent low speed torque. Can drive many loads without gearing.
9) Excellent repeatability. Returns to the same location accurately.
10) Overload safe. Motor cannot be damaged by mechanical overload.
Top Ten DC Servo Advantages:
1) High output power relative to motor size and weight.
2) Encoder determines accuracy and resolution.
3) High efficiency. Can approach 90% at light loads.
4) High torque to inertia ratio. Can rapidly accelerate loads.
5) Has "reserve" power. 2-3 times continuous power for short periods.
6) Has "reserve" torque. 5-10 times rated torque for short periods.
7) Motor stays cool. Current draw proportional to load.
8) Usable high speed torque. Maintains rated torque to 90% of NL RPM
9) Audibly quiet at high speeds.
10) Resonance and vibration free operation.
Top Ten Stepper Disadvantages:
1) Low efficiency. Motor draws substantial power regardless of load.
2) Torque drops rapidly with speed (torque is the inverse of speed).
3) Low accuracy. 1:200 at full load, 1:2000 at light loads.
4) Prone to resonances. Requires microstepping to move smoothly.
5) No feedback to indicate missed steps.
6) Low torque to inertia ratio. Cannot accelerate loads very rapidly.
7) Motor gets very hot in high performance configurations.
8) Motor will not "pick up" after momentary overload.
9) Motor is audibly very noisy at moderate to high speeds.
10) Low output power for size and weight.
Top Ten DC Servo Disadvantages:
1) Requires "tuning" to stabilize feedback loop.
2) Motor "runs away" when something breaks. Safety circuits required.
3) Complex. Requires encoder.
4) Brush wearout limits life to 2,000 hrs. Service is then required.
5) Peak torque is limited to a 1% duty cycle.
6) Motor can be damaged by sustained overload.
7) Bewildering choice of motors, encoders, servodrives.
8) Power supply current 10 times average to use peak torque. See (5).
9) Motor develops peak power at higher speeds. Gearing often required.
10) Poor motor cooling. Ventilated motors are easily contaminated.