new and context

[Noeck]

Hi,

what is the difference between \new and \context?
I have read 5.1.2 Creating contexts, but I don't understand it yet.

It talks about 3 commands for a context:
  \new type music expression
  \context type = id music
  \context type music

Why is \new type = id music not listed with an extra bullet? Or, why is
\context type = id and \new type = id is not?

Where would I need \context?
There is an example:
 <<
  \new Staff \context Voice = "A" \music
  \context Voice = "A" \arts
 >>
But I could write \new Staff << \music \\ \arts >>, couldn't I?

Ok, I see some differences in the stem directions, but it's not clear to
me why. I would be very happy, if anyone could explain that to me.

Would a syntax be possible without new and LilyPond creates the context
if it is not there and references an exising one, if it has the same
name? Like:
 <<
   Staff { music }
   Staff <<
     Voice = "one" { music }
     Voice = "two" { music }
   >>
   Lyrics \lyricsto "one" { lyrics }
 >>

Cheers,
Joram