What differences are there between the Magical Girl Lyrical Nanoha anime and manga?
Nothing! The aforementioned manga provides minor additional background for fans. This includes:


Magical Girl Lyrical Nanoha MOVIE 1st THE COMICS
Magical Girl Lyrical Nanoha A's
Mahou Shoujo Lyrical Nanoha StrikerS THE COMICS


The remaining manga continues with an unique story:


Mahou Shoujo Lyrical Nanoha ViVid
Mahou Shoujo Lyrical Nanoha Force


The former is a carefree spin-off focusing on Vivio (but fun!), while the latter continues Nanoha's story.