Cold sores can be manifestation of HSV 1 or HSV 2 infection.
When they are result of HSV 2, they tend to be milder case of cold sores (HSV 2 is not so strong when it isn't at its site of preference, genitals; it is same for HSV 1)

ok. thanks so much for the reply.

Do cold sores stick around forever? Like they heal but remain dormant then come back?

i think so. i think if you have cold sores, you have hsv1. it lies dormant but you can have outbreaks and reccurances.