Jesus and the Holy Spirit are Identified as Distinct Persons in Acts 10:38

how God anointed Jesus of Nazareth with the Holy Spirit and with power. He went about doing good and healing all who were oppressed by the devil, for God was with him.

In support of the biblical doctrine that the persons of the trinity are distinct from one another we find Peter speaking of both Jesus and the Holy Spirit as distinct persons.

This is in contrast to heretical teachings such as Modalism (which teaches that only one divine person exists who expresses himself at different times in different modes).