Is your copy of music from the iTunes store the same as mine?
iTunes removed DRM from it's music catalog in 2009, so I'm wondering if your question is about iTunes at all? If not, you might be better off specifying what DRM scheme you have a question about.

That said, iTunes used FairPlay for DRM before, and as explained here, it does generate a unique key for every user. So, it will indeed be different for every customer. The same should be true for all DRM schemes, since if the customer could not be identified from the data inside the DRM scheme, it would defeat the purpose of DRM to start with.

It is also worth noting that while DRM was removed from iTunes, current downloads still contain your Apple ID in the downloaded file. However, tool exists to remove this meta-data from the media.