I have generally heard people describe Borg's forehand grip as Eastern but at 1:20 in this video he describes it as Western. Also, his preparation and follow through is close (for that era) to the modern forehand.
Interesting video. Looks to me like his FH grip is what today in US is called an Eastern grip maybe shaded somewhat toward semi Western. And he uses a big loop to get the topspin he was known for. It is certainly not what would be called a full Western grip today in US. I've read that outside of US grips sometimes have different definitions than what we customarily use.
I don't know, in some shots it looks his racquet is all the way back down (i.e pancake) and that is how he demonstrated it. What is possible is at the time of contact he may be moving his grip up closer to an Eastern.
It was a Western in 70s, anything more closed than Continental was called Western. There's commentary at USO 1980? by T Trabert saying the same, so it seems that was the terminology of the time.
So if a Eastern was called a Western where do you go from there? What's a Semi West, West etc.
Once players used more than one grip for all shots, continental, new definitions where developed. This also occurred on BH.
There was discussion that Western was named after West Coast USA where it developed. But cant confirm or denial this. Though seemed that Continental or Hammer or Handshake grip was nearly exclusive pre 70s.
End of the day he used what we now identify as Eastern.