Unix Command to List files containing string but *NOT* containing another string

Try this:

grep -rl <string-to-match> | xargs grep -L <string-not-to-match>

Explanation: grep -lr makes grep recursively (r) output a list (l) of all files that contain <string-to-match>. xargs loops over these files, calling grep -L on each one of them. grep -L will only output the filename when the file does not contain <string-not-to-match>.