Ok, that one. That looks to be the same idea as Makita Hypoid Gear Grease.
If you're looking for the same grease, good luck. All of these manufacturers have the blends made to proprietary specs, just so you're locked in. Stihl is about as bad as it gets when it comes to lock in.
Any gearbox that contains a worm or helical gear, requires a special lubricant that has friction modifiers to prevent wear from a lot of sliding action (that's not the case with a traditional gearbox).
So, that's the reason that going with a plain grease is a bad idea.