I’m already confused about the Rhino renders. 
In Rhino, there seems to be just one render.
Rhino Render in v6 is the off-line renderer (also sometimes called production renderer). This is pretty much the same renderer as in v5, with some improvements.
The Raytraced viewport mode is indeed using a very different engine called Cycles. The engine is an open source production raytrace engine from Blender 3D. The settings you can find in Tools > Options | Cycles are for that Raytraced viewport mode. This gives you an interactive viewport integration of that Cycles engine. If you have a fairly recent GPU (Kepler and newer architectures for Nvidia GPUs, and at least GCN 2nd generation for AMD GPUs) Cycles, and thus Raytraced can take advantage of that GPU to accellerate the raytracing.
In the future (v7) the Cycles engine will replace the old Rhino Render engine. This isn’t done yet, but will be in the near future. Once that is done the Rhino Render will be exactly the same as the Raytraced viewport.
If you have any specific questions feel free to ask them.
So good. And what works when you click the Render button (from the drop-down list above)? Otherwise, where is Cycles used in Rhino?
The _Render command starts whatever is set as the Current Renderer. In the case of your screenshot Rhino Render.
But if you have any other plug-in installed and set as Current Renderer it will be that.
The default Rhino has Raytraced using Cycles, along with _ViewCapture* commands used on a Raytraced viewport.
In v6 it is already possible to get Cycles doing a production rendering as the Current Renderer: search for Rhino Render Next or rhino-render-next on this forum.
