When using motor oil, I would recommend non-detergent oil (not the detergent oil that you put in your car). The reason is that detergent oils are designed to soak up moisture (from surfaces or air) when cool, but the give it back up when heated to operating temperatures as in automotive engines, where the vapor is carried away by the crank-case ventilation system. Machine tool bearings, etc. that do not get very hot, or non-ventilated crank-case engines generally should not use detergent oil, since it will eventually saturate with moisture and can then cause corrosion. Non-detergent oil does not absorb moisture, but displaces it, which works better in an environment that does not heat up regularly or is not ventilated when it does heat up.
I don't know whether synthetic oils have the same moisture absorbing capabilities without detergents (or if they are available without detergents), so this may not apply to them.
And of course if you regularly clean and re-lube your firearms, this may not matter as much unless you intend to store the firearm unused for a potentially extended period of time.
Andy