they are both the same thing (a hydraulic oil) with the exception of the ATF has the friction modifiers so when it gets squeezed out of the clutch packs the friction material grips instead of slides.
I've been involved with industrial conveyance lift equipment which literally ran a couple million cycles just on normal ISO-32 mobil hydraulic fluid. Never changed, was still running perfectly after 12 years in production. In my mind that's an application which is not in the same ballpark of severity as an automotive lift which might see, like 10-12 cycles per day? This, maxed out was a ~2000 lb lift, around 36", 70x per hour. There's other servo-hydraulic equipment I've worked on which has a huge rack of controllers, a 50hp motor on the pump, the cylinder rods are around 4" dia, and it uses....ISO-32 mobil hydraulic fluid.
So I would trust the normal hydraulic fluid. There's no clutch packs. ATF might be a more widely available (before Tractor Supply) product, that most everyone familiar with vehicles can source. I think there's still ISO-32, 46, and 68 hydraulic fluids, so some variability there. I will try to source Mobil when my lift arrives, due to my experience with their products in my work.