ADC stands for Analog to Digital Converter which is a general term covering all forms of such converters. Types of ADCs incude Sucessive-Approximation, Integrating Ramp, and Sigma-Delta. ADCs are used when you want to convert an analog signal into digital form (generally a series of digital numbers).
PWM stands for Pulse Width Modulation, a type of digital modulator, which converts an analog signal into a series of digital pulses. It's commonly used in switch-mode DC power supplies and class-D audio power amplifiers. It's also often used by microcontrollers as a simple way to generate an arbitrary analog signal by filtering the pulses. The average value of the pulses equals the desired analog voltage.