Does the White Album 2 anime share the same storyline as the visual novel? I want to start watching the White Album 2 anime but I want to play the VN also. 

I heard that the story from the anime is different than the game. Is this true? Because I would rather play the game first if it's the same story, but if it's an new anime original story I will watch it first.
Yes, the anime does take some liberties between the two. The visual novel and anime do follow more or less the same path in the end and do converge but there are some differences.
However, note that the plots remain fairly similar despite this. I haven't looked at the next Visual Novel after Introductory Chapter yet but since they both end fairly similar one can imagine that the differences aren't large enough that you couldn't skip Introductory Chapter and go straight to the next chapter after watching the anime.
The differences are large enough that the Baka Tsuki project does not want anyone translating purely off the anime:

Can I use stuff based on what I've seen in the anime?
Not really... the anime takes its liberties with the adaptation, even
though it's done very well. There are some aspects that are shared
between the game and anime, but please don't try a 1:1 copy of
anything in-between.

It's worth noting White Album 2's Introductory Chapter (the arc in which the anime covers is kinetic. This means there will not be choices to make and it will be fairly linear. So, divergence will not be massive.
That said, I'll leave this as it is and keep spoilers out. If so desired, I can add more information under a spoiler tag listing some major differences.