Apparently you've misread the manual. The -u flag is for unified context, not Unicode and -c is for copied context, not 'Context format':
-c -C NUM --context[=NUM]
Output NUM (default 3) lines of copied context.
-u -U NUM --unified[=NUM]
Output NUM (default 3) lines of unified context.
The most straightforward way to find out what is the difference, is to try it out:
$ cat >1
line
diff
more
^D
$ cat >2
line
ffid
more
^D
$ diff -c 1 2
*** 1 2010-12-14 09:08:48.019797000 +0200
--- 2 2010-12-14 09:08:56.029797001 +0200
***************
*** 1,3 ****
line
! diff
more
--- 1,3 ----
line
! ffid
more
$ diff -u 1 2
--- 1 2010-12-14 09:08:48.019797000 +0200
+++ 2 2010-12-14 09:08:56.029797001 +0200
@@ -1,3 +1,3 @@
line
-diff
+ffid
more
Do you get what's the difference?