Is there a standard definition of what it means to S2S?
....S2S is "Surfaced 2 Sides...

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.

....The wood is roughsawn and banded, or
dimensioned and then banded. The wood can
warp, twist, cup, etc. but if it has been surfaced
to S2S the surfaces, no matter how distorted the
board is, are parallel....

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?

....Yes it is, and no it's not. A little quick lesson
here. Wood has a specific cut: "To grade", and
"Through & Through". The wood is then hand graded for grain, figure, color,
and defect. At
this point the wood is usually still flat. The wood
is then surfaced to grade: "Hit & Miss, S1S, S2S,
S3S, S4S, SS-PTS, finish (the later two are
plywood grades). Not surfaced is called rough
sawn. The grading can also take place after
the wood is surfaced, and just before it is
packaged for delivery. Depends on the mill, how
they process, age of the mill, size of the operation.

The wood can then be air and or then kiln dried.
The wood is dried by weight to a specific
moisture content, when drying, it is stacked,
stickered, spaced, and banded. The period of
initial drying subjects the wood to much tension.
The banding is to keep the wood from distorting.
As the wood dries, it shrinks and the banding is
thus loosened. The movement at this point is
reduced, but the wood still prone to distortion.
A surfaced board can distort but still be parallel.

My preference is to select my trees, assist the
sawyer and cut for grade. Air dry to about 25%
(I live in the desert). The wood can then be
further dried to 12% in a solar kiln. A solor kiln is
not used comercially because they are too slow,
however, they heat and then cool. This daily
cycle help relieve the internal stress in the wood.
This makes it possible to keep degrade as low as
3% (yes, really!).
By air drying the wood myself, I can set the
thickness of the spacers and stickers to determine
how fast the wood is to dry. I can also keep
checking the wood for weight and shrinkage and
keep tensioning the chain binders. This helps
reduce degrade. The advantages of processing
my own wood are that I know exactly what wood
I have (ever bought Honduras Mahogany? You
may have bought H.M, but were actually sold
African Mahogany). I can also select the cut, and
dimension. This greatly reduces waste as I get
the wood sized to the projects. Strict control
over the drying gets me a better wood. Usually no
case hardening (though I have had some problem
with Black Walnut) or internal stresses. Also, the
cost is much lower. The down side is that I need
a way to fell, transport, cut, dry, and store the
material. This all takes time, knowledge, tools,
and space. I also need the knowledge of how to
grade if i intend to sell any of my private stash.

To finish answering your question, no, S4S is not
any flatter. That is a matter of wood movement,
not surfacing. "S4S means Surfaced 4 Sides".
If the surface is dimensioned, it is dimensioned. If
it distorts, it distorts.

To me it is always better to select and process my
own wood, but then I have the background (the
lumber industry, followed by the construction, and
then millwork industry) and the resources. Most
of my fellow woodworkers are stuck with lumber
yards or worse yet the big box stores with high-
priced wood that is processed to look saleable,
and generate the highest dollar.

Just my 2 cents...
-Rick Buchanan