I think it is likely to do with the history of how and why the modes have been developed.
Others can explain better but the viewport mode that is called ‘rendered’ is rendered a bit like a computer game, ie the lighting is an unrealistic fudge and, I imagine, rendered by the GPU.
Using the render tool has traditionally used the rhino render engine which uses the CPU to calculate a higher quality image based more accurately on the lighting within the scene. I’m not sure what rendering technique has been used historically here but I don’t think it is raytraced. It appears to similar in some ways to the scanline renderer I used to use in another app years ago. This has always been far too slow to have as a live viewport display mode. It is also not as good as raytracing.
It is only fairly recently that raytracing could conceivably be performed in real time or near real-time. This, in theory should hopefully allow the two other tools / modes to be mothballed in due course which would remove the undeniable confusion that comes from there being two different images styles produced using tools called ‘render’ and a third by a tool called ‘raytrace’.
Now for hoping that raytrace mode and rendering speeds up a bit because the performance on my pretty new Mac is still really bad! I have to remember (this is vitally important) to not save and close a file with raytrace display mode activated. If I forget, the file takes FOREVER to load as Rhino prepares and starts rendering the raytraced view. So so painful.