How is the more formal nature of a draft different from the informal nature of pre-writing?

Pre-writing is the same as brainstorming.  This means a
few things.  First of all - anything and everything goes.  It is an opportunity to get
every single thought down on paper - even the bad ones that will never make it into the
draft.  Prewriting is best done quickly - and can be written in the same way you might
take notes.  This means shorthand is okay, lists are okay, arrows and circles connecting
ideas are encouraged, scratching out and underlining, all of these things are allowed in
the pre-writing process.

The draft however, even if it is
simply an initial or rough draft - should be written formally - meaning, in complete
sentences which are hopefully organized into paragraphs.  A rough draft does not need to
be perfect, understandably it could go through several changes, but it should be written
in the way the final paper is going to look and sound.

This
is why I encourage my students to write very complete outlines (also part of
pre-writing).  By the time you get to the drafting stage - you do not want to be making
major organizational changes.  It is almost too difficult to do when reading a paper in
full sentences and paragraphs.  It is much easier to look at the skeleton and see where
entire sections need to be tweaked, moved, or completely cut.  It is also easier to see
in the later parts of the pre-writing stage - major points that may be missing.  Once
your paper is in the rough draft stage - it might seem very long (and no doubt, possibly
tedius by this point) - so noticing major holes is a little harder to
do.