[Uncle Bob]

Grease (typical paste texture not spray, get to that in a minute) is basically a sponge full of oil. Most formulations are 90 - 95% oil plus additives and the soap thickener; e.g. lithium, sodium, barium, etc. The oil component has a viscosity just like fluid oils, and varies by application similarly. The thickener is needed to assist in keeping the oil in place when inadequate containment for fluid is the situation. But the basics are still the same, it's the oil component that does the lubricating, not necessarily the thickener. Which brings us to the spray stuff. Likely what you've used has a very light oil and a very fluid "sponge" for sprayability, and in the kind of application you've described you probably got very little actual lubricating material in a light spray application. Not necessarily a problem in some apps, just means more frequent application is necessary to have enough oil to do the job.

Mitch's suggestions are reasonable alternatives, though on something like the vice screw you might be better served by an oil with a tackiness additive, such as bar and chain oil used for chainsaws. The drawback there is that any work debris might get caught up in the lubricant. Depends on how you use the equipment.