It adds an index arm and artificial horizon to the instrument, and was invented by English sea captain John Elton, who patented his design in 1728 and published details of the instrument in the Philosophical Transactions of the Royal Society in 1732.
The significant differences are the change in the upper arc to a simple triangular frame and the addition of an index arm.
In addition, at the mid-span of the label there is a mounting point for a lantern to be used during nocturnal observations.
Set the label so that the Sun's image is projected on the shield at the hole with the index arm roughly horizontal.
This is a means of measuring altitude of a celestial object that is very different from what can be done with a Davis quadrant.
Set the label to a position that will put the object to be measured within the range of the instrument.
Elton had the misfortune to invent his instrument in the same period of time as the octant.
Given that Elton's quadrant was roughly as complex as an octant in construction, there would not likely be a significant advantage in price.