Rear derailleurs are the part on the back of the bike frame that move the chain up and down the cassette when the rider wants to change gears. Rear derailleurs can either be cable actuated (mechanical), electronic, or hydraulic in nature, and range from 3-13 speeds.
Front derailleurs shift the chain in the front section of the drivetrain from the smaller chainrings to the larger, or vice versa. Front derailleurs are either cable activated (mechanical) or electronic in nature. Front derailleurs come in either 2 or 3 speed variants depending on whether the bike has a 2x or 3x drivetrain.