Thats not all. If you have a very efficient mixer, you might also see the difference frequency mixed with the sum frequency and its sum and difference mixed with one of the two originals. In other words, depending on the quality of your mixing device and the strength of the signals that are present you have the ability to generate thousands of new frequencies. A receiver operating anywhere near these mixes can hear them as if they were a valid signal. The fact is, they are a valid signal.
Mixes can take place in any device that acts as a diode.
You may hear it referred to as a non linear device. A transmitter final, a receiver front end, a water contaminated connector can all present a place to mix. Let's look at it another way. Suppose you had two pianos. Both were located right next to each other.