PA, microphones and live vocals are all commonly linked by one factor - the human voice. A PA system is used to process and amplify the human voice as well as other musical and rhythmical instruments. Likewise, microphones are part of the process and are the interface between the voice and the amplifier.
By definition a PA (Public Address) system is a collection of amplifiers, speakers, a mixer and one or more microphones. These items are used to amplify speech or vocal announcements or the playback of music and other recorded sources. It is typically used within large halls, auditorium or a sports stadium to relay information or to provide entertainment for those gathered there.
Larger PA systems are referred to as 'Sound Reinforcement Systems' and these are the type that would be utilised for live music events or theatre in venues of an appropriate size. Microphones come in many styles and categories and can be hard-wired or wireless depending on their application. Most microphones used to 'close mic' acoustic instruments tend to be hard wired whilst many lead vocal, theatrical and TV broadcast microphones are wireless.