At first, these are not greeting words. 'zao shang' -> 'morning', 'wan shang' -> 'evening', 'zhong wu' -> 'noon', 'xia wu' -> 'afternoon'.
'shang' in this word is '上' means 'up', 'wu' in this word is '午' means 'noon'.
Generally, in Chinese, you can't tear the word apart to single characters and try to understand the meaning of the word.