The difference between phonemic awareness and phonics is that phonemic awareness is a crucial element of phonics, which is a specific manner in which people are taught how to read.
Phonemic awareness is the term given to the ability of listeners to be aware of the different units of sound, or the phonemes, that we use in the English langauge to differentiate meaning. For example, picking a word and identifying the way that we can separate it into three separate phonemes, such as "cat" being made up of three different sounds, requires phonemic awareness.
Phonemic awareness thus is recognised as the basis for learning phonics, which is a method for teachign reading and writing by helping learners to develop and advance in their own phonemic awareness. Research indicates that learners with higher phonemic awareness are able to learn how to read and write more quickly, though this is not free from controversy. In particular, the nature of the English language and the way that so many words are written in a way that does not correspond to the phonemes makes this an approach that does receive some criticism.