> The Xbox music store serves as both a music player as well as a music store.
Yet it's called the "Xbox Music Store" making it very clear where their priorities lie. iTunes is iTunes and can also access the iTunes Store. It's not "iTunes Store, Play Music Also".
> I don't consider showing content from the store as advertising.
> Is iTunes also "a big advert"?
Nope, because the line between the iTunes Store and iTunes is quite clear. It ends when you click that "iTunes Store" link in the sidebar. Up until then, you'll see no advertisements or artists promoted.
Is the iTunes Store a big advert? Definitely. However it's a store, most are plastered with advertising. That is normal.
Ads in your music player isn't normal. If you're willing to accept it, that's completely different and entirely your prerogative. Many others feel they already absorb plenty of advertising and aren't interested in providing new avenues to reach them, especially ones through products that they paid for.
Considering that streaming is free (w/ ads) showing content from the store I'd argue makes a lot of sense. Spotify does the same thing.
With that said, iTunes has added "In the Store" picks in iTunes... while I'm sure you'd argue that it's distinct, given how seamless it is integrated in the new iTunes UI, I think most people won't view it as much different than the XBox Music Store -- and even worse in some regards since you can stream for free from the XBox Music Store.