Marcus,
Ok, I think my confusion started when google displayed google as www but then it redirected to https. I've recently found out this happens when your logged in to google so that explains that.
One last question, if I change my certificate to WWW will my SERP show this or will it still say https://www.mysite.com. If I want to get rid of https from showing will that mean I have to take the certificate from the homepage and just have it on the relevant pages of my website?