Based on the erotic game by Lune.

How different is the Fairy Tail manga from the anime?

It has more differences than you think.
It's true that the anime tries to stay faithful to the manga but even only in the first volume there are many differences. First, the manga isn't afraid to show a little blood.
The anime only shows bruises.
Example time! Remember in the second episode when Mirajane is crushed by Elfman in a comedic way? Well, in the manga she gets hit with a bottle to the head and is seen bleeding (she's totally unfazed though).
And that episode when Macao returns to normal after being defeated by Natsu, he just has a few bruises.
In the manga, he has a deep cut on his torso and Natsu uses his fire to painfully seal the wound. Also, Gray is seen smoking.
Yes, this 17 year old smokes in public.
You don't see that in the anime, do you? And also the design of Natsu's scarf in the manga resembles scales and in the anime it's just squares. These differences all appear in the first volume of the manga.