You have identified the main difference. The instrument used for the ablation may also differ depending on what is used in the OR versus the office, but the main difference is that one is done under anesthesia in the OR and the other is not. At UCSF, we typically reserve the OR for (1) really really extensive cases (eg lots of warts or very diffuse HSIL) or (2) cases of suspected cancer where we need to perform an excision to either make the diagnosis, or in cases of extremely small cancers, offer surgical excision as the definitive treatment. 

HRA guided ablation is most often performed in the office, but can be performed under sedation or even general anesthesia.  The choice of tools to ablate the HSIL is varied according to the surgeon performing HRA- some gynecologists use CO2 lasers, some surgeons use an electrosurgical generator to fulgurate the tissue, some will excise the lesion if they think it could be a superficially invasive squamous cell carcinoma of the anus.  As long as the treatment gets through the entire thickness of the lesion without damaging the anal sphincter, it should be adequate. 

Cristina Brickman and Jessica Korman