At one time, automotive gearboxes and rear axles used SAE 90 or the Hypoid derivatives, but with the advent of front wheel drive and no bevel or hypoid gears, the need has gone away. Modern car gearboxes seem to run quite happily of whatever oil is in the engine. Engine oils contain all sorts of additives to prevent oxidation at high temperatures, frothing and viscosity improvers, as well as detergents. None of these are likely to be needed if used in the gearbox of a lathe or milling machine, but probably won't do any damage either.
Hypoid oils can be reactive, containing sulphur compounds which react with the gears, to attach themselves to the running surfaces to reduce friction.
Machine oils are likely to be less sophisticated than engine oils, since the temperatures are lower (I hope that no machine runs with an oil temperature in excess of 100C!), and possibly apart from rubbing pressures on the gears, the pressures will be lower.
So, at a pinch, you would probably get away with using an automotive oil. It may even work out cheaper to buy 5 litres of SAE 10W/30 than a small quantity of something specific! HERESY!!!
Howard