A Stepper Motor is a type of electric motor.
A Servo Motor is a motor WITH a control mechanism.
A servo motor has a mechanically coupled position feedback & will control/drive to a position. They can have built-in control electronics, where you send a control signal (could be a control voltage eg 0-5v, or a square wave 0-100% duty cycle) & the servo motor will drive to a position proportional to the control signal (ie 0%, 50%, 100%, or any value in between). Servo motor outputs are generally geared down, the final output could be a shaft that rotates through an arc of 90 deg, or a linear drive via a rack or chain. Example of Servo Motors are "RC servos" used in Radio Controlled model aircraft, or the linear pen drive in a analogue electric chart recorder.
A Stepper motor is a particular design of electric motor that is driven via pulses, where each pulse represents a fixed angular rotation (eg 7.5 degrees of rotation per pulse). They are used where precise small steps are required. Commonly used in printers & scanners. Can be used as a Servo Motor - if position feedback is incorporated.