A receiver comprises 3 things:  a preamplifier (which has the multiple inputs, and selects between them); a power amplifier, which supplies enough power to drive speakers; and a tuner, for radio.

That's the classic combination.  Current day receivers have variations - some may include or not include a phono preamplifier, which takes turntable/cartridge output and boosts it up to "line" level voltage, which is the level that other sources (tuner, CD, tape, tv) output.  Some modern receivers also have digital to analog converters (DAC's) built in, so one can plug in a purely digital source (through USB or other means).  And you prob already know that many/most modern day receivers are mulit-channel, not just stereo, since they are usually sold with a multi-channel "home theatre" system in mind.

An "integrated" ampliifer combines a preamplifier with a power amplifier.  Thus an integrated is a receiver, minus the radio tuner.

 A TUNER is the actual RECEIVING device that receives AM or FM broadcast signals using an antenna.

An Integrated amplifier has switching circuits to select a tuner, CD player, turntable, or other sound source, and also has low-level amplification circuits (preamp), and high-level power amplifier circuits to drive speakers (amplifier/power amp).

A RECEIVER combines the tuner and integrated amplifier in one unit.

IF YOU HAVE A SEPARATE AMPLIFIER (power amplifier, that is), you need a PREAMP to go with it, since a basic amplifier has no input switching or volume control, and a PREAMP provides these.

A " cable box" or a "satellite box" is a video receiver that receives microwave signals from a cable or satellites and converts them to a baseband video signal that a TV can receive with its built-in circuits.

Of course a TV set is also a television RECEIVER that can receive TV signals from an antenna using its own channel tuner circuitry, but most people don't use antennas anymore.