Realizing that this is all so subjective, and with the usual disclaimer of YMMV:
I agree with
grim that the terms 'socially acceptable', DFS, BBS, dolphin smooth, etc. are bandied about as if they are defined terms of art. I think each shaver will have their own idea of what they mean.
I tend to go for three kinds of shave: the first is a close shave, which for me involves 2 passes and some touch up. My definition of it is that there is absolutely no stubble when feeling the face and neck with the grain, and some feeling of a little stubble here and there when feeling against the grain.
The second is a very close shave. For me, this involves three passes and touch up. This is where I can't feel any stubble when feeling either with or against the grain.
The third is a super close shave. I can get this with 4 passes-an extra North-South pass to start-and touch up with buffing, etc. In this shave, there's no feeling of stubble whatsoever even when pressing firmly in an against-the-grain direction.
The soap/shaving mix I use will depend on what kind of shave I want to achieve.
If it's really hot out (it was 112F/44C yesterday here, more of the same today), and I need to spend time outside, I'm not going for the super or even very close shave, it's just uncomfortable. If I have to be on camera, I want a shave that's close, but with products-both soap and after shave products that are more astringent than oily so I don't get a 'shiny' face.
In all cases, I'm going for a shave with no irritation or excessive feeling of the skin being 'raw'.
The soap/shaving mix I use will be determined by all of the above. For a close shave, a good quality soap is all it takes: My go-tos are Nuávia, MdC, Barrister & Mann, and some other good artisan soaps that I've been exploring.
If I'm going for a very close shave, I find that I'll need something extra to make the shave comfortable: For me, it's a bit of oil added directly to the mix after face lathering for the first pass.
For the super close shave, it's soap, oil, and then I'll add a bit of a compatible cream-a small dollop does the trick. I usually just apply this by hand to the mix that's already on the face, and face lather. This combination allows me to do an extra pass and enough touch up to get the beard and all stubble in all directions so I can't feel it.
It may be counter intuitive, but I find the soap is most important if I'm going for the simple close shave-it's just the one product and the shave fails or succeeds on that one product. The more closely I want to shave, the more additions to the mix, the individual components become less critical, and it's the combination that allows me to shave away until my heart's content.
I find it difficult to stop sometimes at a simple close shave. That's when I get into a bit of trouble. Say I just want a simple two-pass and touch up shave and decide to use just the soap, and then I go back and do lots of touch up, I find that using just the soap, even the really good performers, can leave me with a raw-and sometimes red-face.
All of the above is, of course, dependent on a good razor and blade, a good technique with appropriate pressure, etc. But with that as a given, the soap/shaving mix will dictate the kind of closeness I can achieve.