The 1019 is to 2004 as 1016 is to 1015. The 1019 will fit in a 1016 box, just as the 2004 will fit in a 1015 box.
If you’re looking for the short-length offset-shank coupler, you want the 2004. You can fit it in a 2004 box or a 1015 box, depending upon the mounting height on your model. The 2004 box is approximately 1/16” thinner in height than the 1015 box.
Also, it is possible to mount a 1019 in a 1015 box, but the coupler would have more vertical flex than if in a 1016 box. But it will work as the location of the centering spring on both coupler arms is the same.