This is what I know:
HPV type 16 causes both oral cancer (mostly oropharyngeal but some larynx as well) and cervical cancer. HPV is also implicated in cancers throughout the genital region (penis, anus, vulva etc).

Because type 16 and 18 can cause cancer, they are classified as a "high risk" types along with a couple of other numbers which I can't recall right now.

We need to keep things in perspective and remember that most people who become infected with HPV - even the "high risk" types do not progress to cancer.

Most people who become infected with HPV overcome the infection and do not get cancer.

This is what I am guessing:
People who progress to cancer may have been unable to clear the HPV infection for some reason so it sits there and can, over time either cause cancer, or allow some other mechanism the opportunity to cause cancer.

Type 16 seems to get all the bad press so this might be the most common of the nasty ones, or maybe it is the easier one to test for ???