There are two basic types of Wireless Microphones
Bodypack Transmitters are Used for Lavaliere or “Lapel” . . . 
Lavaliere Microphones, often called “Lapel Mics” or “Clip-On Mics” are a very popular form factor for presenters and public speakers who want the ability to move above with their hands free.
Lavalieres are excellent for situations requiring “invisible” microphones. These also work well for novice / occasional presenters who are uncomfortable with holding a microphone in their hand or wearing something on their head.
The down side to Lavalieres is that they are more prone to feedback and typically provide less signal then a Handheld or Earset. Having said that – a good sound engineer with the right equipment should have no problem implementing a Lavaliere mic.
. . . and Earset or Microboom Mics
Earset or MicroBoom microphones – often called “Countryman Mics” after Carl Countryman , one of the early innovators of the technology and President and Chief Engineer of Countryman & Associates of Menlo Park, California. These microphones clip to either one ear or both, and typically offer a much better signal that Lavaliere mics simply due to the closer proximity to the speakers mouth.
Earset mics are excellent for public speaking as well as theatrical performances. There even models designed to work well for robust singing voices.
The down side to Earset mics is getting used to something “hanging from your ear”. There is a tendency to want to reach up and touch it to make sure it is still there correctly.
Handheld Transmitters are used for the traditional Microphone style.
Handheld Transmitters provide the most wide-ranging assortment of applications. The nature and design make them the easiest to use by the “Do it Yourself” person or beginner sound engineer. There are a wide variety Microphone “Elements” available. The element is the end of the microphone, usually round or conical . (in the image above it is silver in color) Different elements work better for different applications. Handheld Transmitters work best when held directly ion front of the mount or sound hole of the thing being amplified – rather than off to the side or hanging down at the waist.
Handheld Transmitters are excellent for any application. They are the easiest to use without feedback, and are very efficient in situations where the microphone will be shared by multiple users (passed around).
The down side to Handheld Transmitters is that they are bulkier and are not easily concealed. Also the benefit of the handheld mic can be negated if the person does not hold it in the correct position.,