Per the Vatican:
237 The Trinity is a
mystery of faith in the strict sense, one of the "mysteries that are hidden in God, which can never be known unless they are revealed by God".58 To be sure, God has left traces of his Trinitarian being in his work of creation and in his Revelation throughout the Old Testament. But his inmost Being as Holy Trinity is a mystery that is inaccessible to reason alone or even to Israel's faith before the Incarnation of God's Son and the sending of the Holy Spirit.
[ basis in faith ]
251 In order to articulate the dogma of the Trinity, the Church had to develop her own terminology with the help of certain notions of philosophical origin: "substance", "person" or "hypostasis", "relation" and so on. In doing this, she did not submit the faith to human wisdom, but gave a new and unprecedented meaning to these terms, which from then on would be used to signify an ineffable mystery, "infinitely beyond all that we can humanly understand".82
252 The Church uses (I) the term "
substance" (rendered also at times by "essence" or "nature") to designate the divine being in its
unity, (II) the term "
person" or "hypostasis" to designate
the Father, Son and Holy Spirit in the real distinction among them, and (III) the term "
relation" to designate the fact that their
distinction lies in the relationship of each to the others.
237 The Trinity is a mystery of faith in the strict sense, one of the "mysteries that are hidden in God, which can never be known unless they are revealed by God".58 To be sure, God has left traces of his Trinitarian being in his work of creation and in his Revelation throughout the Old Testament. But his inmost Being as Holy Trinity is a mystery that is inaccessible to reason alone or even to Israel's faith before the Incarnation of God's Son and the sending of the Holy Spirit.
[ definition of terms ]
233 Christians are baptized in the name of the Father and of the Son and of the Holy Spirit: not in their names,55 for
there is only one God, the almighty Father, his only Son and the Holy Spirit: the Most Holy Trinity.
[ one God ]
253 The Trinity is One. We do not confess three Gods, but
one God in three persons, the "consubstantial Trinity".83 The divine persons do not share the one divinity among themselves but
each of them is God whole and entire: "The Father is that which the Son is, the Son that which the Father is, the Father and the Son that which the Holy Spirit is, i.e. by nature one God."84 In the words of the Fourth Lateran Council (1215), "Each of the persons is that supreme reality, viz., the divine substance, essence or nature."85
[ one God in three persons but, each one is God Himself ]
254 The divine persons are really
distinct from one another. "God is one but not solitary."86 "Father", "Son", "Holy Spirit" are not simply names designating modalities of the divine being, for they are really distinct from one another: "He is not the Father who is the Son, nor is the Son he who is the Father, nor is the Holy Spirit he who is the Father or the Son."87 They are distinct from one another in their relations of origin: "It is the Father who generates, the Son who is begotten, and the Holy Spirit who proceeds."88 The divine Unity is Triune.
255 The divine persons are relative to one another. Because it does not divide the divine unity,
the real distinction of the persons from one another resides solely in the relationships which relate them to one another: "In the relational names of the persons the Father is related to the Son, the Son to the Father, and the Holy Spirit to both.
While they are called three persons in view of their relations, we believe in one nature or substance."89 Indeed "everything (in them) is one where there is no opposition of relationship."90 "Because of that unity the Father is wholly in the Son and wholly in the Holy Spirit; the Son is wholly in the Father and wholly in the Holy Spirit; the Holy Spirit is wholly in the Father and wholly in the Son."91
[ they are distinct from each other by their relation to one another ]
[
http://www.vatican.va/archive/catechism/p1s2c1p2.htm]