Is there a standard definition of what it means to S2S?

Standard technique to get 2 faces surfaced is to joint an edge, then
joint a face, then plane the opposite face. Thus to S2S such that a
board is flat, you've really S3S (or S2S1E as I've seen used).

Seems to me that if you just S2S you've got 2 faces parallel but the
board isn't necessarily flat - it could have a bow or twist that isn't
removed by planing the 2 faces.

So what I really want to know is ... is S2S lumber flat enough for
precision work without further flattening, such as to make a picture
frame or cabinet door frame? If not, is S4S any flatter?

Thanks,
Michael