Re: Shodokan, Tomiki, Aikikai?
That's basically it. The name Shodokan has become associated with a particular curriculum and place so there was some reason for maintaining a broader description in the minds of some, particularly a few of Nariyama Shihan's sempai. In Japan that function was provided by the Japan Aikido Association which is now completely Shodokan.
I think one of the more interesting aspects of Tomiki's Aikido is the strongly developed curriculum and how it evolved. Several well respected non-Japanese Aikidoists learned from Tomiki in the 50s and early 60s and teach in that way. Shodokan Aikido developed continuously while Tomiki was alive and to an extent still does. I think this is one of the reasons the Tomiki designation still exists.
But again - what really matters is what happens on the mat.