“Eques” is the Latin word for knight, and the CCR does translate it that way. The idea is that the eques is not only an active soldier for Christ, as he promised he would be when he was confirmed; nor only that that he is an active soldier for Christ the King and the doctrine thereof, an upholder of His social reign, as the miles is. Rather, the eques fundamentally changes his life on behalf of the social reign of Christ the King.
The eques turns a large part of his life toward the service of Christ the King. He prays at least seven times a day; he prays for the success of the restoration of the social reign of Christ the King; he fasts; he thus provides an immense service to the King. And for this, he receives no public recognition beyond that of a miles—he knows that his reward is with that King, in Heaven.
The eques of the CCR makes certain promises regarding his prayer and his works:
The eques has the same rights and duties as the miles; there is no independent recognition, separate insignia, or any other sign of distinction. Indeed, it is quite likely that no one would know a eques from a miles unless the individual volunteered the information. It is an internal commitment made privately for an eternal reward.
A summary of membership rules is available.
Christus vincit! Christus regnat! Christus imperat!