Amplifier usually means an integrated amplifier, with switching for a number of inputs, volume (and often tone) controls, and a power amplifier section to drive loudspeakers
Preamp = preamplifier. As above but minus the stage used to drive the speakers, so needs to be used with a...
Power amp = power amplifier. Used with a preamp, purely provides the gain to drive the speakers, but all the control stuff is done by the preamp. Power amps can be monobloc (ie mono, so two needed for stereo), stereo (ie two channels) or multichannel for use in home cinema applications.
Receiver = as integrated amplifier, but with a radio tuner built-in
AV receiver = as receiver, but with surround sound processing onboard.