At the very least only state exchange plans have the subsidy. In CA, exchange plans for at least one carrier (Anthem) have a limited provider list as compared to their private plan.
In that case it is not the same plan. If I go to ehealthinsurance.com for my zip it returns plans that conform to ACA. I suspect that those plans would be available via the healthcare.gov web site.
As I mentioned before, each state can have there own set of rules so what may be valid in one state may not be in another.