AM is amplitude Modulation, and FM is Frequency Modulation. With both AM and FM, a carrier wave must be broadcasted. And it is just that... A carrier wave for the information. A greyhound bus for the information you are trying to tune in. (music, etc.). The carrier wave is at a particular frequency, which is singled out as you tune in your radio station. All other frequencies are filtered out.

Simplified explanation:

The difference is how the "information" rides on that carrier frequency. And the names give it away. In AM or Amplitude Modulation, the information is added to the amplitude of the carrier signal. When your receiver receives the signal, it does an analog sample of the wave to determine it's average strength, then demodulates the differences in the amplitude to pull out the original information. This is the worst and most inaccurate way of demodulation, for the signal strength is continuously changing, with the analog demodulator always working "behind the times". This is why it took so many years for the occurance of AM Stereo. It's hard enough to accurately pull one stream of info out of the carrier wave. Try pulling two distinct signals out of one carrier wave that is Amplitude modulated. How in the world do you do that??? (But they do have AM stereo now, yet not very popular) The reason it came first, is it is very easy to mix amplitudes, and no complicated circuitry was required in the old days to pull in the correct carrier wave. They couldn't do frequency modulation at first cause uncle sam wouldn't let commercial businesses transmit on high enough frequencies to pull out the original information. Also since AM carrier waves have relatively low frequencies, they can travel quite a distance.

In Frequency Modulation, the information is added to the frequency of the carrier wave. The amplitude of the incoming signal is a mute point as long as it is strong enough where your receiver can lock onto the carrier wave. Carrier frequencies in high ranges were released for commercial use, so they could transmit in the MegaHertz range. Since all information needed in the hearing range is commonly in the 20 to 20KiloHertz range, it was easy to pull the signal in. The information didn't cause enough of a difference in the signal to cause the tuner to filter it out. And since the original carrier frequency is known, and locked in, it was extremely easy to pull out the original information. In fact, you could add 6 or 8 different information signals if you wanted to. Complex, but achievable. Since the demodulation is so accurate, this gives it better clarity, and the ability to modulate 2 separate signals for stereo. However, since the carrier frequency is so high, it bounces off obstacles instead of going through them, thus reducing range.

Let's see if I can make the difference more clear:

For AM radio, imagine a sine wave swinging back and forth at a single frequency. That is the 'carrier wave'. Now imagine the peaks of those waves being different heights. Then draw a continuous curve between those wave peaks.

That curve represents the audio signal. The tuner converts that curve into a voltage signal that drives a speaker.

http://www.electronics-radio.com/.../am.php

For FM radio, imagine that you are graphing the instantaneous *frequency* of the carrier signal, which is centered around a single 'station' but is varying above and below that value. That continuous frequency change represents the audio signal. The FM tuner outputs a voltage proportional to that frequency that drives a speaker.

http://www.electronics-radio.com/.../fm.php

AM radio has the advantage of transmitting further than FM, especially at night when AM signals will bounce off of the upper atmosphere.

FM radio has the advantage of being inherently more resistant to noise and interference and can produce a higher-fidelity audio signal.
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The difference between AM and FM radio is that FM has shorter range, within the line of sight of the radio transmitter.