There seems to be still be a lot of debate and arguing regarding this form, and to this day most people can agree that the anime and manga are different continuities, yet when it comes to this concept, all of a sudden the anime and manga become one of the same.
♫ Let's get started! ♫
'A Goku Black version of Super Saiyan', this suggests that this could either be his literal version of regular Super Saiyan, or a unique different Super Saiyan. Now one person argued that 'Super Saiyan' is an umbrella term used for most Super Saiyan forms in Super, however I beg to differ on this one.
SSGSS has as far as I know, been insinuated to as a 'God form', or the umbrella term being 'Super Saiyan God', I haven't gone back and watched passed the Future Trunks Arc, so there's a possibility SSGSS may have been referred to as 'Super Saiyan' just once, but I do not recall this happening. Here are some screenshots of numerous times characters referred to SSGSS as 'Super Saiyan God';
Another argument is that Super Saiyan 2 was referred to as 'Super Saiyan', but this isn't all that true, the only time Super Saiyan 2 was referred to as 'Super Saiyan' is when it probably wasn't "clear" as to whether it was actually Super Saiyan 2 or not. When they want to emphasize a specific form, they will refer to it by it's name, otherwise I have a suspicion that there were times where Super Saiyan 2 was used but it wasn't the intention as you can see by the scripts. I think this is the case because they probably didn't have a design or Super Saiyan 2 Trunks so they decided to keep the regular hair styles but put emphasis on that it was still SSJ2 in the dialogue.
The next episode Goku goes into Super Saiyan 2 once again when he fights Goku Black, in which he has the correct design. Goku Black comments on him going Super Saiyan, but doesn't mention it to be the next level up from Super Saiyan, which Black would probably most likely know about.
Now one could say that it's just the case of another umbrella term, but I just find that very strange that exactly after it was referred to as Super Saiyan 2 in the previous episode, all of a sudden it's being referred to as just 'Super Saiyan'.
More proof for Goku Black actually turning into a form that isn't quite SSGSS is that he imprinted on Goku while Goku was in Super Saiyan(2?):
Goku Black even starts to what I assume to be him becoming more like Goku by learning to use his power. It's very similar to the opening of the show.
Take what you want from those images.
There is a piece of evidence that could be the leading factor to Super Saiyan Rosé being SSGSS in the anime instead of Super Saiyan (or another version of Super Saiyan), Future Trunks comments that it looks like Goku Black has seen Super Saiyan Blue before.
However, it is possible that the Zamasu that took Goku's body had seen Blue already on God Tube. As Goku Black reveals that he was defeated by the Goku of his timeline:
The manga and the anime are different continuities with slightly different logic or lore, yet people still want to use the manga as the source explanation for Goku Black's unique form, even though it's been implied to be his own Super Saiyan version form that's unique to him. If you want to still go by quotes on the series, then it's even stated that Goku Black turned into a "Super Saiyan", not "Super Saiyan God", even though his form still has god ki, but the characters acknowledge it to be different.
Now it is true that in Toriyama's notes he stated this:
Goku Black can go Super Saiyan and a Super Saiyan of a slightly different hair color than Goku. This is extremely vague information, my own theory is that Toei thought Toriyama meant that Goku Black turned into a literal Super Saiyan with a different hair color.
We did get a proper explanation from Toyotaro for Goku Black's form in the manga.
Again, the anime and manga are separate, and cannot and should not be used to explain each others story points. You can argue Toyotaro gets more information than Toei and his story line is a lot closer to the original vision, which in my mind is true, but it doesn't change the fact Toei's adaptation is different and has basically established that.
I used to think this didn't make any sense, but in a way it does the more I think about it. Toriyama stated that he doesn't think Goku would still use Super Saiyan 2 & 3, instead he'd master his Super Saiyan form to surpass those successors.
This is my own head canon so take it with a pinch of salt; Zamasu was already a fighting prodigy, learning more about Goku's body as he used it.
Goku Black in my opinion probably knew of the other Super Saiyan forms, and instead decided to master Goku's power like he stated, then reach his own 'perfect' and 'beautiful' version of Super Saiyan. What backs this up is Black's showing no strain in this form, and is significantly more powerful, he really has mastered
Goku's power. (Again this is my own head canon).
I certainly do wish we saw Toriyama's version, I'd love to know whether it was more like Toei's version, or Toyotaro's version, or perhaps he'd surprise us with something different!
Anyhow, that's it, if anyone has any counter arguments, any sources proving this to be wrong, please share them. I've searched high and low for sources stating that Goku Black's Rosé form to be anything other than a "Goku Black version of Super Saiyan"