The output format from "git-diff-index", "git-diff-tree" and
"git-diff-files" are very similar.

These commands all compare two sets of things; what is 
compared differs:

git-diff-index <tree-ish>::
        compares the <tree-ish> and the files on the filesystem.

git-diff-index --cached <tree-ish>::
        compares the <tree-ish> and the index.

git-diff-tree [-r] <tree-ish-1> <tree-ish-2> [<pattern>...]::
        compares the trees named by the two arguments.

git-diff-files [<pattern>...]::
        compares the index and the files on the filesystem.


An output line is formatted this way:

------------------------------------------------
in-place edit  :100644 100644 bcd1234... 0123456... M file0
copy-edit      :100644 100644 abcd123... 1234567... C68 file1 file2
rename-edit    :100644 100644 abcd123... 1234567... R86 file1 file3
create         :000000 100644 0000000... 1234567... A file4
delete         :100644 000000 1234567... 0000000... D file5
unmerged       :000000 000000 0000000... 0000000... U file6
------------------------------------------------

That is, from the left to the right:

. a colon.
. mode for "src"; 000000 if creation or unmerged.
. a space.
. mode for "dst"; 000000 if deletion or unmerged.
. a space.
. sha1 for "src"; 0\{40\} if creation or unmerged.
. a space.
. sha1 for "dst"; 0\{40\} if creation, unmerged or "look at work tree".
. a space.
. status, followed by optional "score" number.
. a tab or a NUL when '-z' option is used.
. path for "src"
. a tab or a NUL when '-z' option is used; only exists for C or R.
. path for "dst"; only exists for C or R.
. an LF or a NUL when '-z' option is used, to terminate the record.

<sha1> is shown as all 0's if a file is new on the filesystem
and it is out of sync with the index.

Example:

------------------------------------------------
:100644 100644 5be4a4...... 000000...... M file.c
------------------------------------------------

When `-z` option is not used, TAB, LF, and backslash characters
in pathnames are represented as `\t`, `\n`, and `\\`,
respectively.


Generating patches with -p
--------------------------

When "git-diff-index", "git-diff-tree", or "git-diff-files" are run
with a '-p' option, they do not produce the output described above;
instead they produce a patch file.

The patch generation can be customized at two levels.

1. When the environment variable 'GIT_EXTERNAL_DIFF' is not set,
   these commands internally invoke "diff" like this:

      diff -L a/<path> -L b/<path> -pu <old> <new>
+
For added files, `/dev/null` is used for <old>.  For removed
files, `/dev/null` is used for <new>
+
The "diff" formatting options can be customized via the
environment variable 'GIT_DIFF_OPTS'.  For example, if you
prefer context diff:

      GIT_DIFF_OPTS=-c git-diff-index -p HEAD


2. When the environment variable 'GIT_EXTERNAL_DIFF' is set, the
   program named by it is called, instead of the diff invocation
   described above.
+
For a path that is added, removed, or modified,
'GIT_EXTERNAL_DIFF' is called with 7 parameters:

     path old-file old-hex old-mode new-file new-hex new-mode
+
where:

     <old|new>-file:: are files GIT_EXTERNAL_DIFF can use to read the
                      contents of <old|new>,
     <old|new>-hex:: are the 40-hexdigit SHA1 hashes,
     <old|new>-mode:: are the octal representation of the file modes.

+ 
The file parameters can point at the user's working file
(e.g. `new-file` in "git-diff-files"), `/dev/null` (e.g. `old-file`
when a new file is added), or a temporary file (e.g. `old-file` in the
index).  'GIT_EXTERNAL_DIFF' should not worry about unlinking the
temporary file --- it is removed when 'GIT_EXTERNAL_DIFF' exits.

For a path that is unmerged, 'GIT_EXTERNAL_DIFF' is called with 1
parameter, <path>.


git specific extension to diff format
-------------------------------------

What -p option produces is slightly different from the
traditional diff format.

1.   It is preceded with a "git diff" header, that looks like
     this:

     diff --git a/file1 b/file2
+
The `a/` and `b/` filenames are the same unless rename/copy is
involved.  Especially, even for a creation or a deletion,
`/dev/null` is _not_ used in place of `a/` or `b/` filenames.
+
When rename/copy is involved, `file1` and `file2` show the
name of the source file of the rename/copy and the name of
the file that rename/copy produces, respectively.

2.   It is followed by one or more extended header lines:

       old mode <mode>
       new mode <mode>
       deleted file mode <mode>
       new file mode <mode>
       copy from <path>
       copy to <path>
       rename from <path>
       rename to <path>
       similarity index <number>
       dissimilarity index <number>
       index <hash>..<hash> <mode>

3.  TAB, LF, and backslash characters in pathnames are
    represented as `\t`, `\n`, and `\\`, respectively.


combined diff format
--------------------

git-diff-tree and git-diff-files can take '-c' or '--cc' option
to produce 'combined diff', which looks like this:

------------
diff --combined describe.c
@@@ +98,7 @@@
   return (a_date > b_date) ? -1 : (a_date == b_date) ? 0 : 1;
  }

- static void describe(char *arg)
 -static void describe(struct commit *cmit, int last_one)
++static void describe(char *arg, int last_one)
  {
 +     unsigned char sha1[20];
 +     struct commit *cmit;
------------

Unlike the traditional 'unified' diff format, which shows two
files A and B with a single column that has `-` (minus --
appears in A but removed in B), `+` (plus -- missing in A but
added to B), or ` ` (space -- unchanged) prefix, this format
compares two or more files file1, file2,... with one file X, and
shows how X differs from each of fileN.  One column for each of
fileN is prepended to the output line to note how X's line is
different from it.

A `-` character in the column N means that the line appears in
fileN but it does not appear in the last file.  A `+` character
in the column N means that the line appears in the last file,
and fileN does not have that line.

In the above example output, the function signature was changed
from both files (hence two `-` removals from both file1 and
file2, plus `++` to mean one line that was added does not appear
in either file1 nor file2).  Also two other lines are the same
from file1 but do not appear in file2 (hence prefixed with ` +`).

When shown by `git diff-tree -c`, it compares the parents of a
merge commit with the merge result (i.e. file1..fileN are the
parents).  When shown by `git diff-files -c`, it compares the
two unresolved merge parents with the working tree file
(i.e. file1 is stage 2 aka "our version", file2 is stage 3 aka
"their version").