Cold sore herpes is different from genital herpes.
From CDC:
What is the link between genital herpes and oral herpes (cold sores on the mouth)?
Oral herpes (such as cold sores or fever blisters on or around the mouth) is usually caused by HSV-1. Most people are infected with HSV-1 during childhood from non-sexual contact. For example, people can get infected from a kiss from a relative or friend with oral herpes. More than half of the population in the U.S. has HSV-1, even if they don’t show any signs or symptoms. HSV-1 can also be spread from the mouth to the genitals through oral sex. This is why some cases of genital herpes are caused by HSV-1.
HSV1 can be genital as well, and a baby born during an infection outbreak in the genital area could contract the herpes virus as it’s being born
[[More than half of the population in the U.S. has HSV-1]]
I’ve read that 90+% have it