The manga follows the main story line of the game. However, there are a few differences, such as characters appearing in places they haven't appeared in the game and also, Regal does join the party you just never see him fight. A few of the other characters are like this also. Battles and dungeons are also made shorter and boss battles pass by quite quickly. Reading the manga, you can understand the main storyline but it leaves out some of the littler things and doesn't even mention quite a few of the dungeans or Summon Spirits.
The anime, much like the manga, is a shortened version of the game. It is still ongoing with 8 episodes currently out. The first part of it is called the Sylvarant Episodes. They take place from the beginning when Lloyd and Colette set out on their journey until when they escape from the Renegades into the world of Tethe Alla.
The 2nd part of the series called the Tethe Alla episodes take place from crash landing in Tethe Alla until they rescue Colette from Rodyle.
There has also been a 3rd set of episodes that are going to be released in late Nov. 2011 entitled The United World will presumably cover the rest of the game after the Tethe Alla episodes.