lube compatibility chart?

Not car related but it could be. I know that no OEM (cars, lawn equip, heavy machinery etc) drills and bottles their own lubricants. but it would be nice to know that for instance Mopar XXXXXXX that is recommended in the service manual is actually Shell YYY. or Exxon. or whatever.

I have a late -'80s/early '90s Woods zero turn mower here (same as a Grasshopper) that I want to swap out the hydro fluid in. Problem being the Woods fluid is $37/QUART! that's a $80 oil change with tax and all. I E mailed Grasshopper and they gave me "their" OE fluid number. not much help.
I need to know if "regular" Trans-hydro fluid would be the same.
for reference I have a Woods number of 70776 and a Grasshopper number 345044. I have no clue as to whether these 2 hydro fluids are the same or not. I'm looking at compatibility with seals, hoses and stuff.
Author: volaredon