In a nutshell:
"New Religions" emerge from Great World Religions when "revelations" or religious experiences are received via prophets or sages. "New Religions" either enhance an existing tradition by revealing something that was not known previously or break away from an existing tradition if an "error" is revealed and a new, sub-sect is created.
"New Religions" can be considered a "distant cousin" of a previously established religion.
Meta-narratives (traditional stories) keep the community (followers of a particular religion) united and connected.
"New Age Religions" began to emerge in response to globalization (the ability to access information on most of the religions in the world), and modernity. These "New Age" movements are a result of global religious diversity, technology, and modern science, and they challenge the "purity of tradition.
"New Age" movements are considered "eclectic" such that people who are "New Age" pick and choose through beliefs, practices, and aesthetic aspects of Great World Religions, "New Religions", primal religions, and have a particular interest in the metaphysical and shamanism.
"New Age" people seek out the meaning and significance of life and time and their place in it; they are more focused on the self rather than the "truths" established by traditional religions.