Is super saiyan god a "super saiyan" transformation, or does just it have a missleading name? After watching the trailer of the new Dragon Ball movie, where a villain with an armor similar to saiyans appear and it has yellow eyes, 



I started to wonder if a super saiyan transformation can have eyes of a different color than blue, so I started to check,

SSJ1, USSJ, SSJ2, SSJ3, blue eyes,
SS Rage, blue eyes,
Legendary SS , blue eyes,
SS Blue, blue eyes,
SS Blue evolution, blue eyes,

SS Rosé, pink eyes, but I'm not sure if this counts because it comes from a half god / half saiyan,
Ultra Instinct grey eyes, but apparently this isnt a super saiyan transformation, but a form any race can get,
SSJ4 yellow eyes but it's non canon,

And the only one that's left is super saiyan god with red eyes, but is this transformation a real "super saiyan" transformation or it's just a missleading name? Super Saiyan Blue is attained by "getting the power of a super saiyan god and transforming into a super saiyan" . So how can you transform into a super saiyan if you already have the power of a "super saiyan" god? Wouldnt this mean the "super saiyan" god is a missleading name and it isnt a "super saiyan" transformation but another kind of saiyan transformation?
The Super Saiyan God transformation requires the power of 6 pure hearted Saiyans. However it is not mentioned anywhere that the 6 Saiyans must be Super-Saiyan themselves, (since Videl's unborn child was able to contribute as well). 

I think it gets very confusing though because all the Saiyans during the ritual including Goku were super-Saiyans(except Videl's child) and yet Videl's hair-color also changed to Golden. So I think the name Super Saiyan God is a misnomer and it should have actually been Saiyan God. 

It would also make sense that way, since Super Saiyan Blue would then technically be a "Saiyan God" who does a Super-Saiyan transformation. That would be more accurate, but I guess we have to accept Akira Toriyama's naming convention, since it is his creation after all.