Letter of Recommendation from Governor's School Summer Program teachers/professors

No, it would not replace a teacher recommendation. Many colleges (especially on the common app) have a section for additional recs from a coach, EC teacher, etc. It would be the same process as uploading for a regular teacher.
As for teachers vs the professor, go with teachers. Teachers are likely going to be preferred, and many colleges that require a LOR will require it to be from a teacher. The seniority of a professor doesn’t matter if they don’t know the applicant that well, since it’s the applicant they’re looking at, not the recommender.
Have your son look into the colleges he’s interested in and see if they have specific requirements. Some colleges, like MIT, require LORs from certain subject teachers, while other just want any teachers.