Bitdefender Free and root certificate

My understanding is that many AV's including Bitdefender Free install their own root certificate for scanning SSL websites. I don't want to debate whether this is good or bad. Instead I wanted to know how it works. On some websites, when I view the certificate, it shows that it was issued by Bitdefender. However, on other websites, it shows the certificate issued by a different entity. Why does Bitdefender Free uses its own certificate on some, but not all websites when my protection is on?