$ git diff            (1)
$ git diff --cached   (2)
$ git diff HEAD       (3)

1. changes in the working tree since your last git-update-index. 2. changes between the index and your last commit; what you would be committing if you run "git commit" without "-a" option. 3. changes in the working tree since your last commit; what you would be committing if you run "git commit -a"

$ git diff test            (1)
$ git diff HEAD -- ./test  (2)
$ git diff HEAD^ HEAD      (3)

1. instead of using the tip of the current branch, compare with the tip of "test" branch. 2. instead of comparing with the tip of "test" branch, compare with the tip of the current branch, but limit the comparison to the file "test". 3. compare the version before the last commit and the last commit.

$ git diff --diff-filter=MRC            (1)
$ git diff --name-status -r             (2)
$ git diff arch/i386 include/asm-i386   (3)

1. show only modification, rename and copy, but not addition nor deletion. 2. show only names and the nature of change, but not actual diff output. --name-status disables usual patch generation which in turn also disables recursive behavior, so without -r you would only see the directory name if there is a change in a file in a subdirectory. 3. limit diff output to named subtrees.

$ git diff --find-copies-harder -B -C  (1)
$ git diff -R                          (2)

1. spend extra cycles to find renames, copies and complete rewrites (very expensive). 2. output diff in reverse.