I don't think so. Anyone can join Facebook. Ping requires an iTunes account. Ping is more like trying to keep people sticking around so they'll buy more. Apple is clearly leveraging the power of person-to-person recommendations over algorithms. It will be interesting when Ping adds books.
I would say Apple is trying to compete more with last.fm and maybe even myspace. A lot of musicians use myspace as their social networking to communicate with their fans. I can easily see Ping being used for the same purpose and being tied into iTunes will help out the musicians a lot.
Considering that it only features songs bought on iTunes and has a strong bias towards artists right now (normal users can't do status updates as far as I can tell), it created it to increase sales under the consumer benefit of music discovery.
I wouldn't say they're so much competing with myspace or last.fm as they're poised to dominate a wide open space hobbled by those two companies poor execution. Nonetheless, I effectively agree with danishkhan.
looks like Zune + Zpass+ Zune social to me. Now that all the zune stuff and music subscriptions will ship with the phone,etc... Seems like competition will be though and Apple would be behind if they didn't have a subscription/recommendation/social offering.