Ive just noticed it, when I access my site using [mysiteurl.org...] then I get the ads relevant to my keyword. But when i only use [mysiteurl.org...] (without the www) i got PSA or other unrelevant ads..
Google considers each of these to be a different page, so our crawlers will index each page separately. It sounds like one of your pages may not have been crawled yet, leading to less relevant ads appearing.
It you've just pasted the code, give our crawlers a couple of days to index both of your pages. The ads should become more relevant with time.