Phonological awareness is the ability to recognize that words are made up of a variety of sound units (phonemes). So you can identify syllables and see smaller words within larger words (for example, cat in catalog).
On the other hand, while the phonemic also involves an understanding of the ways that sounds function in words, it deals with only one aspect of sound: the phoneme. So, for example, in the word ball there are three phonemes /b/, /aw/, /l/. If you replace B with W, you will get a completely new word - wall.