Why are some anime series so different from their manga counterparts, and vice versa?

Most of the time it's a corporate decision; they are trying to make the anime/manga more interesting than the original to obtain more viewers/ratings. The more ratings, the more money the corporation makes. Sometimes it an artist decision; say if it's because an artist is trying to make it easier on themselves with artwork and deadlines and things, or if the artist wants a story to go a different way that he/she deems better or more fitting. But most of the time it's a corporate decision.

1. A comic book, is the authors original intent. It could be in specialty stores.

2. When a comic book is animated it is limited to the folllowing.

A. Censorship on television, advertisment.

B. The Animators abilities to animate ( since animators are trained to draw in a specific manor )

C. Time, Money.

D. If the audio was recorded after or first.

E. Everything over all together.

The animation is the exact same thing, as the comic book. Sometimes the author fills in gaps. Some animations are done without the authors help and could be derailed from story but keeps a reasonable idea. In most cases, movies, and OVA ( which are movies ) is done outside the story.

Sometimes the anime catches up to the manga and instead of making filler episodes and completely ruining the show, they decide to have the anime go it's own way.

ie. Fullmetal Alchemist (2003)