Do You Need Surgery to Fix a Stage 2 Overbite/jet?

I can see why you are reaching out to have your question answered. It sounds like your second opinion orthodontist did not mention the need for surgery, but the partner of your old orthodontist did? My recommendation is to contact these doctors again, to have them clarify their opinion. They will likely want to take updated photographs, x-rays and models, if you haven't had those done recently. Typically those records are shared between offices, if you request it.

Some orthodontic terminology below:

Phase One - early interceptive ortho around age 8-10 for initial correction of bite and alignment issues.

Phase Two - full ortho after the Phase I, to complete alignment of all the teeth, typically around age 12-14.

Class One: normal bite

Class Two: lower teeth bite too far back, excessive overjet

Class Three: lower teeth bite too far forward, underbite

There is no such thing as a stage 2 problem in orthodontics...sometimes we do treatment in stages, so we call initial treatment (before all the permanent teeth erupt) as stage 1 and then a second phase (or stage) when  all the teeth come in.

As to whether you need surgery to fully correct your problem, that requires a full diagnostic work-up and consultation with the orthodontist...if you don't have faith in the one you are seeing get a second opinion