They are one and the same. The Father, the Son, and the Holy Spirit are all of one essence (God), and yet are distinct. Don't ask me to explain. Some things about God just can't be explained (otherwise, He wouldn't be God!).
Both Protestants and Catholics pray and worship the Father, the Son, and the Holy Spirit. Because all three persons (persona, not phyiscal persons but essence of or being) is equally God.