There are many organizations and Orders which form part of the widespread fraternity of Freemasonry, each having its own structure and terminology. Collectively these may be referred to as Masonic bodies, Masonic orders or appendant bodies (or orders) of Freemasonry.
The basic unit of Freemasonry is the Masonic Lodge, which alone can "make" (initiate) a Freemason. Such lodges are controlled by a Grand Lodge with national or regional authority for all lodges within its territory. A masonic lodge confers the three masonic degrees of Entered Apprentice, Fellowcraft, and Master Mason.
In some countries, notably the United States of America, there are also organizations affiliated with Freemasonry which admit both Master Masons and non-Masons who have some relation to a Master Mason, such as the Order of the Eastern Star, International Order of Job's Daughters (Job's Daughters International) and the Order of the Amaranth. Still other affiliated organizations like the Order of DeMolay and the International Order of the Rainbow for Girls admit non-Masons and have no requirement that an applicant be related to a Master Mason.
These are the "Concordant Bodies" referenced herein.