Catholic
The Catholic Church teaches that God is one divine essence in three distinct persons — Father, Son, and Holy Spirit — coeternal, coequal, and consubstantial. It holds that the Son is eternally begotten of the Father, and the Holy Spirit proceeds from the Father and the Son (filioque).
Source: CCC 245–248; 253–256; 266 ↗
Orthodox
The Orthodox Church teaches one God in three hypostases — Father, Son, and Holy Spirit — of one essence, confessed in the Nicene Creed. It holds that the Holy Spirit proceeds from the Father alone, rejecting the filioque as an unauthorized addition that distorts the Trinity's inner life.
Source: The Orthodox Faith, Vol. I — Holy Spirit ↗
Lutheran
Lutherans confess with the ancient Church that there is one divine essence in three persons — Father, Son, and Holy Spirit — as defined at Nicaea. They hold the Nicene Creed — as confessed in the Western form with the filioque — as a true and binding exposition of Scripture's teaching on God.
Source: Augsburg Confession, Art. I ↗
Reformed
The Reformed tradition teaches that in the unity of the Godhead there are three persons of one substance, power, and eternity: God the Father, God the Son, and God the Holy Ghost. It holds that the Father is of none, the Son is eternally begotten of the Father, and the Spirit eternally proceeds from both.
Source: Westminster Confession 2.3 ↗
Baptist
Baptists teach that the eternal triune God reveals himself as Father, Son, and Holy Spirit, with distinct personal attributes, but without division of nature, essence, or being. They hold that there is one and only one living and true God, infinite in holiness and all other perfections.
Source: BFM 2000, II ↗
Methodist
Methodists teach that there is one living and true God, everlasting, of infinite power, wisdom, and goodness — and that in the unity of this Godhead there are three persons of one substance, power, and eternity: Father, Son, and Holy Ghost. They hold the historic creeds as faithful summaries of this mystery.
Source: Articles of Religion, Art. I; UMC What We Believe ↗