Are genital herpes and mouth herpes the same?

if my partner has a cold sore and gives it to me, can I pass it to his genitals by giving oral sex or is that a different kind of herpes ?

No they are not. The herpes sores (commonly called cold sores) you can get on your lips and inside the mouth are Herpes Simplex 1 and Genital Herpes are Herpes Simplex 2. They are two different strains of the herpes virus. Chicken pox is also a strand of a herpes virus.

Same answer as above. A cold sore can be passed to someone else though, so best get it treated. Once you have genital herpes though, it is always in your system and is always transferrable, especially on a break out. Its an STD. People with genitle herpes must alway use a condom.