What is the difference between anaphora and parallelism?
Parallelism is the consistent use of a particular grammatical form/structure throughout a sentence. Anaphora is the purposeful use of repetition to create a dramatic effect.
I like reading and writing.
I need food, but I also need shelter.
"It was the best of times, it was the worst of times, it was the age of wisdom, it was the age of foolishness, it was the epoch of belief, it was the epoch of incredulity, it was the season of light, it was the season of darkness, it was the spring of hope, it was the winter of despair." -Charles Dickens, A Tale of Two Cities
Anaphoras use parallel structure deliberately, in an attempt to emphasize/highlight the words. Dickens's quote uses it to compare and contrast pairs of things (wisdom and foolishness, light and darkness, etc.).
Parallel structure is simply keeping the same basic format throughout a sentence. It is not trying to create a dramatic/rhetoric effect.