The wireless system is responsible for transmitting the sound captured by the microphone or headmic to the music system. They are always formed by a transmitter, which is the one we connect the microphone or headmic to and a receiver, which is the one we will connect to the mixer of our sound system.
There are several types depending on the transmission: VHF, UHF, Digital. They can also be fixed or variable frequency. The fixed frequency ones are configured in a transmission frequency, so each transmitter works only with its receiver. The variable frequency systems, however, have several transmission channels (between 4 and hundreds, depending on the quality) so that to work properly, the transmitter and the receiver have to be tuned in the same channel. The main advantage of these systems is that you can have a receiver and several transmitters, or if you have several systems (one in each activity room, for example) you can use any of the transmitter with any of the receivers, simply tuning the same channel.
It also depends on the number of available channels the number of sets that can operate simultaneously in the same installation without interference between them. For example, the Shure PG14E system has 10 channels, but we can only have up to 4 systems working at the same time if we do not want interference between them.