In pistols it's really not that big of a deal, ironically I often use Amsoil 20w-50 Motorcycle oil as that is what I run in my bike or whatever other synthetic motor oil I have on hand. Any Group III or IV based synthetic motor oil is more than sufficient for a pistol and way cheaper than any gun lube. All a lube really has to be on a pistol is 'there'. The difference in performance of specific lubricants is really mostly measured by how often you need to reapply, and how easy/hard it will be to clean the gun later. I would not be afraid to use nearly any lube if it was all I could get my hands on in a class or during a range session, as I have had to in the past.
Synthetics (Group IV and Group III base stocks to a slightly lesser extent) usually have less volatility and will evaporate more slowly (storage/carrying) and 'burn off' when hot more slowly (while shooting). This isn't to say the base stock itself is 'better' necessarily in this specific parameter, but a function of base stock performance in conjunction with the total additive package. The synthetics usually have very good corrosion inhibition performance and tend to have robust detergent and dispersant packages to allow easier cleaning. As far as mechanical removal by slide cyling, it doesn't matter much what you use, enough slide cycles will remove the bulk of any lubricant.
In my experience, blowback actions like .22s tend to like a much thinner lube, especially in cold weather.
Greases tend to separate in storage, even when stored on your gun (see ASTM D1742-06 Standard if you need help sleeping). They can also adversely effect function in cold weather. I do not recommend them, but that is not to say they won't 'work' to a reasonable extent. It's just not an optimum application for that type of lube IMO.
An AR is a different animal, but that is beyond the scope of this thread.
Hope this helps.