In practice, subject_id = person_id. This is because the OHDSI software that are based on the cohort framework have been written for a patient/person as the unit of analysis.
Please review these posts for relevant past discussions. Bottom line, not many in the community have pushed for use cases where a care_site or provider_id is the unit of analysis. In those use cases, provider_id/care_site_id may become the subject_id. To allow for this interchangability, the term “subject_id” was used. Some have proposed to eliminate this ambiguity and use person_id uniformly.