Many Ariens use a 00 oil which is an amalgem of an aluminum looking paste combined with lighter oil in their NON cast iron drive boxes. Its only available from Ariens as I looked elsewhere w/o luck. If your gearcase is 2 pieces this is probably the lube you want. Put as much in as you can because you can't damage it with an overfill. Putting straight EP grease in there isn't a good idea.
H2- I have a similar looking grease in the little single speed gear drive trans on my Honda pushmower. I popped the bottom of the case off after years of use and that grease looked new yet.