As stated above, ...ISO is the International Organization for Standardization, SAE is the Society of Automotive Engineers.
As pointed out, you can cross the numbers, and the simple version is that; the bigger the number, the thicker the oil with ISO, and SAE both. But the scales are different.
Hydraulic 32 is pretty light, ISO 150 is like honey. Tap heavy is like refrigerated molasses.
Correct, sulfides are hypoid agents, and they do work well. Old school. They do stink as the sulphur atoms get stripped off, as it leaves a "Sulphur" without a home. Rotten eggs, burnt matches. But synthetics still have hypoid agents, they are just synthetic polyesters, (and stuff), so with gear lubes, they still offer hypoid protection, they just don't stink anymore, and don't coke up.
Bear in mind, that my suggestion takes into account, that standard motor oil is about the same viscosity as way lube 68, (a little thicker). When you do the math on surface area of a dovetail way or a gib, and the adhesive qualities of scraped ways, the pressure per square inch, and adhesion of the ways, makes light work of an oil that is designed for high loads and high temps (motor oil).
Motor oil is always on the shelf in most garages, relatively cheap, and it is as easy as grabbing some off the shelf, at least at my house. It also holds another virtue when living in winter climates with machines in cold garages, motor oil is "chemically enhanced" to simulate the virtues of a thinner oil at lower temperatures. IE, 5W(Winter)-30. Which means the oil acts as a thinner oil at cold temps (short version, lol) . Normal machine shop oils are single weight oils. When I need to mill something quickly, and it's 20 degrees F in the garage, I don't want to crank through molasses, nor bog down the table feed motor, nor wait 8 hours for everything to come up to temp. ;D
I haven't been here long enough to say for sure, but I am betting you won't find many takers that will tell you to put "anything but" what the manufacturer recommends in a 1 year old machine that is large enough for a wet gearbox, and wet spindle. It matters not, what we'd do, it's your call. But... I prefer using what is on my shelf, for home shop purposes. So long as it's "as good or better" than what comes out of it, I'll run that. If you don't know for sure, and aren't trained in oils, use what they tell you to use, error to the safe side.
Your initial question made it sound like you were running basic used shop equipment with some miles on it, like many of us. and availability and price seemed to be the question. "is it good enough".
... Brand new stuff with a warranty is 100% your call. But without even looking up the exact specs, I'd put my money on a synthetic motor oil, and synthetic SAE gear lube, across the board, when compared to most way lubes et al.. There are some way lubes that are better than others, but mostly they are disposable cheap oils. #68 is pretty much just the weight of the oil, you can buy cheap 68 in any brand, or the buy the good stuff... But it's not an extreme duty oil by comparison.
Remember this too, most (if not all) big CNC's, which use 68, have ball bearing linear guides, not ways and gibs. Different deal from a basic mill. But why wouldn't they recommend it, since it's available in every machine shop? ...Doesn't mean it's the best, or only, option. In the end, it's always your call though.
Another quick point of view to ponder, is to consider the gearbox in your home shop mill, vs. the gearbox or differential in your vehicle. Which needs severe duty lube more? Of course, the diffy in your truck needs way better hypoid protection, and is in a much harsher environment, ergo, the lube in there has to be pretty good stuff. ...But who would ever put synthetic diffy juice into a machine at the shop, when there is a 55 gallon drum of the recommended oil right there on the shop floor. At home, in the basement, the 55 gallon drum of that lube is not there. So, is there any reason to go out of your way to get it? IMO, No. Just be careful when substituting.