Yeah that's true. Good point. Thanks Alex
The strain of HPV that caused cancer does not cause warts. Having one strain does not mean that you don't have others, but most doctors diagnose warts by visual inspection.
Often the virus that caused genital warts does not present any symptoms, but if she has never had warts, or hasn't had warts in six months, you would be at no more risk for contracting genital warts from her than with any other partner.
Can doctors tell what kind of strain it is?
This is the community forum. Posters here are not Doctors, just people with simmilar experiences and hopefully a bit of knowledge to share. To get a response from a doctor you should post in the the doctor's STD forum. There is a fee for using this service but many topics can be found through searching the archives.
Active HPV infections are contagious. Whether are not the infection will affect you is a different question. Assuming your girlfriend does not also have the strain that causes genital warts, you have little to worry about. While you can be infected with HPV, it rarely causes problems for men, but men can carry the virus and infect future partners.