Actually, only Dark Horse's English translation uses the term "offshoot" while the original translator for the official translation used the common term, "alter ego."
Hyrule Historia, Page 094 Aria Tanner* | Hyrule Historia, Page 094-DH |
Agahnim
A dark wizard who threw Hyrule into chaos. His true identity is Ganon’s alter ego. | Agahnim (DarkHorse)
A priest of darkness who plunges Hyrule into chaos. In truth, he is an offshoot of Ganon, sent forth from the Dark World. |
*Aria Tanner is GlitterBerri, who was responsible for pages 84 to 239. She has stated her work was edited. Her translations are still available.
Again, pawn was used in the English version, with "alter ego" being the most used term to reference Agahnim. "Offshoot" is a broad term that could be used to imply he is somewhat separate, but also still attached and being part of Ganon. It can also imply being an alter ego. DarkHorse probably chose this term to give canonical but vague information without delving into the debate, or just to sound fancy. Probably the latter, since both translations are using a synonymous term in this case. See below:
The kanji used to refer to Agahnim's role is 分身 (Bunshin) which literally translates as follows:
parturition; delivery; one's child; branch; offshoot; one's other self (alter ego)
Therefore, the term "offshoot" is being used as a synonym for "alter ego." Both translations refer to the same state of being, strongly suggesting that he is indeed an alter ego and not a separate being.