Though I have seen the movies, I am glad I read the first book instead of just skipping it. This way, I can follow the books (considering they are different from the movies.
New Moon picks up right where Twilight left off. I am not of any sort confused although, the book can be hard to follow if you do not start from the beginning of the series. There is not very much explaining in the second book. The author expects you to know the characters, setting, and plot. It is just like a continuation of the first one. Bella and Edward have already been through so much together but are still dealing with new issues everyday which adds to the story. The intensity of the story increases with every book as I've noticed so far.
To sum it up, I am still identifying the differences between the books and Twilight series movies. Also, I am contrasting the first and second books. I am planning to read more in this series because it is something that interests me.