It is possible that to the sensei Akira Toriyama running out of colors to rename character transformations. However, the fact that the word Black be present in a version of Goku and the recent level of friezashown in Dragon Ball Superdoes not mean that both modes are related.
These are two totally different things that we are going to highlight with facts that were presented in the dragon ball super mangain which in addition to having the participation of Akira Toriyama, the illustrator Toyotaro has his hands in it.
Let’s go by parts. black frieza is the most recent appearance of the Emperor of the Universe. After undergoing arduous training in a time room on an unknown planet in Universe 7, the world conqueror arrived refreshed and ready to exact revenge.
It is a transformation with frieza exceeds what was achieved with golden frieza. It is simply an advance in the evolution of the villain who now has black features on his shell, instead of the old purple color that characterized him in Dragon Ball Z.
Goku Black has nothing to do with Black Frieza
From Black only the name, because not even the reasons for the color match. This version of Goku is Samazu, a Kaioshin who took Kakarot’s corpse in Future Trunks’ timeline to execute his evil deeds.
That of Black earns it because he is a dark being and full of evil. Totally different from Frieza, that although he is also evil, the color of his transformation has nothing to do with the underworld or the mystical arts (black magic) that Samazu executed to try to exterminate humanity.
About Black Frieza we know little, since he only appeared at the end of the most recent arc of Dragon Ball Super. So we have a lot to learn about the new world conqueror, but we know that there is nothing related to Goku Black.