To those who are not aware of their Philippine geography, Baguio is within the territory of Benguet Province and Benguet Province is within the territory of Cordillera Administrative Region (CAR). In short, the region where Baguio belong is within CAR.
Cordillera Administrative Region is composed of 6 provinces and 1 chartered city. Namely, Abra, Apayao, Benguet, Ifugao, Kalinga, Mountain Province, and Baguio City.
Although Baguio City is within the province of Benguet, still, Baguio is independent from Benguet Province because it is a chartered city.
I hope that this post clarifies all.