Still struggling with PSAs in Polish having spread like a cancer taking over my website. Now I see that if I type www.mywebsite.com into my browser I get Polish PSAs but if I type mywebsite.com I get relavent ads. WTF? I emailed Goog to ask them why they are torturing me (not really, I just asked if they could shed some light on this strange situation). Waiting for a reply
It happens to me to at my blog, i get completely different ads with the "www" but i'm afraid i can't explain you why that happens
Technicaly, They are two different sites so if you have a dynamic index page, they could be viewed by AdSense at different times and therefore produce different ads.
As YFS said they are different, if your normal traffic goes to xyz.com then those pages will be viewed by adsense and relevant ads will display. If you then go to www. xyz .com which doesn't get any traffic it would be the same as putting up a new page, it may take a few views and some time for the ads to appear on there.