Still confused about context vs. new

[Patrick Horgan]

I see many examples with \context, or \new used in the same place.  I've 
read LM 3.1.1 for example which tells me that if I don't create 
explicitly a \new Staff or \new Voice, they will be created 
automatically, and goes on to refer to that as the implicit creation of 
contexts.  I often see examples that refer to contexts, via something 
like \context ChoirStaff, or \context Staff, that have not been 
explicitly created. Can I assume that they are implicitly created?  
Something like this recent example off the list:
> \version "2.11"
>
> \score {
>   \context ChoirStaff <<
>       \context Staff<<
>           \context Voice = voice \relative c'' { \voiceOne\repeat 
> unfold 200 { e2 }
>           \new Voice \relative c'' { \voiceTwo \repeat unfold 200 { c }}>>
>       \context Lyrics \lyricsto "voice" { \repeat unfold 200 { la }  }
>          \new Staff \relative c   <<
>             \new Voice { \clef "bass" \voiceOne  \repeat unfold 200 { 
> f }   }
>             \new Voice  { \voiceTwo  \repeat unfold 200 { a, } } >>  >>
> \layout { }
> }
Why does it use \context ChoirStaff instead of \new Choirstaff?  Same 
for Staff?  Same for Lyrics.  If I change the \context to \new it works 
identically (I think).  Does it?  If not what's the difference?  How do 
I know when to do which?  If I replace all the \new with \context, the 
music changes.  If I replace all the \context with \new it works fine.  Why?

Is there a difference between:

\score {
   \new ChoirStaff <<
      \new Staff{
         \new Voice<<>>
      }
     \new Staff{
         \new Voice<<>>
   >>
}

and
\score {
   \new ChoirStaff <<
      \new Staff{
         \new Voice<<>>
      }
      \new Staff{
         \context Voice<<>>
      }
 >>
}

Are these referring to implicit always pre-existing contexts, so that 
changing the \context to \new just takes up more memory for nothing and 
the implicit ones are still there?

In  LM  3.4.4 it implies without stating that changing a property of a 
Staff happens within the context of the current staff. i.e. setting 
instrumentName for a staff only affects that staff and goes on to say 
that if you don't specify Staff, then it will affect the default 
context, voice.  I had to try it to see if  \set Staff.instrumentName = 
#"Alto" would work--that was a nice clue, wish the text would have 
spelled that out.  It seems as if the writers know this well, it's part 
of their /context/ <grin;> and they don't spell out things that now, to 
them are obvious.

Farther in LM 3.4.4. they begin using commands to change note heads 
without mentioning contexts at all.  Am I to assume, that they affect a 
default context?  Which is that?  The last thing I read was to be 
careful because the default was Voice.  So am I changing a Voice 
property here when I don't specify context?

I'm sure it's all clear if you already know it, but for me, it's quite 
fuzzy.

Patrick