There is little direct relation between White Album 1 and 2. They are in the same series and have some similar themes, but the plots are unrelated and all the characters are new (as well as a different writer). There are a few references to the original game, mostly in the form of music, and it does take place in the same universe 10 years later, but that's basically all the connections. It isn't at all necessary to be familiar with the original to watch White Album 2.
It should be pointed out that both of the anime adaptations are originally based on visual novels. The few references that did exist in the VN versions could very well be removed from the anime. The original White Album came out in 1998, while White Album 2 ~introductory chapter~ (the part which is being adapted this season) was released in 2010. Given the long gap between the White Album game and anime (2008-2009), there's some speculation that the latter may have been intended to increase hype for White Album 2.