search?q=keywords+keywords&[some other variables]

Most of the referral URLS that I get from Bing have the following syntax:
www.bing.com/search?q=keywords+keywords&[some other variables]

However I just noticed that maybe 10-20% of them are coming in like this:
www.bing.com/url?source=search&[some other variables]&url=http%3A%2F%2Fwww.example.com/user-landing-page-on-my-site&yrktarget=_top&q=keywords+keywords&[some other variables]

The first syntax gives me the keywords the user typed in, but the second actually gives me the keywords the user typed in and their landing page on my site. I was originally unaware of this second kind altogether because I have a customized referral report that filters out URLs containing my domain. But now that I noticed them I want to know why they occur to see if I can get more to occur this way because the second syntax contains more valuable information.

If I go to one of the first URLs, it gives me a typical Bing query page. The second URLs seem to just redirect me to the Bing home page. I'm not sure if it has to do with the kind of search being performed (I also get a few www.bing.com/shopping/search?q= referers) or some other metric.

Does anyone know what causes some referral URLs from Bing to have the /search?q syntax and others to have the /url?source syntax?

P.S. I have verified that I am getting both kinds of URLs from non-advertising clicks.

P.P.S. I am not talking about data in Google Analytics or similar software but the raw $_SERVER['HTTP_REFERER'] value coming from the client's original request.