No, HSV1 and HSV2 are different viruses. You may be infected with HSV1 if you are already infected with HSV2, and vice versa, however, infection with one does not mean you will get the other unless you are exposed.
Chat with our AI personalities
You can get HSV1 on the genitals from receiving oral sex with some one that has cold sores. It's not technically HSV2, but any type of herpes that occurs on the genitals gets called 'genital herpes'.