How Does An Integrated Amp Differ From A Receiver?

The term "receiver" derives from the concept of a radio receiver which typically had facilities for audio amplification for playback. They don't call them tuners in HAM circles. They're receivers. The tuner portion of a good old receiver will consume a quarter to a third of the electronics and they were much better quality than what you get in today's black plastic faced boxes. 

Suddenly I feel quite old knowing this term needs clarification.

If its got a radio-tuning dial it's a RECEIVER!

+1 roberjerman

Since the FM bit is quite simple the price difference between an integrated amplifier and a reciever is often minimal. However, in practice modern receivers often have quite a few additional options that integrated amplifiers lack, such as networking ability, Airplay, (more) digital inputs and even room equalization (e.g the new Yamaha RN803d).
These days FM is quite redundant, given the high quality and broad selection of internet radio stations, particularly at higher bitrates. FM is an antequated technology with many sonic limitations. Internet radio is far from perfect as well, and the failings of the two systems are not directly comparable, of course, but on balance I now prefer internet radio for sound quality, and of course even more for the range of stations from all over the world. And with internet radio sound quality will only go up with increasing bandwith and higher bitrates.