The pathogen causing the STD or STI (I for Infection) is the same whether the host is an adult or an adolescent. The treatment, therefore, is the same as far as the medications used. The need to trace sexual contacts and to treat both partners at the same time is also the same.
There may be a difference though if the adolescent is under the age of consent for sexual activity and the sexual partner is more than two years her senior. Then the sexual activity is statutory rape and needs to be reported to the authorities. The exact ages and requirements to report may vary from state to state and country to country.