First, the members of the Trinity are qualitatively equal in attributes, nature, and glory. While Scripture reveals a voluntary subordination among the divine persons in terms of position or role (for example, the Son submits to the Father; the Spirit proceeds from the Father and the Son), there exists absolutely no subordination (or inferiority) of essence or nature. The persons are therefore equal in being, but subordinate only in role or position.
Second, the members of the Trinity are both eternally and simultaneously distinct as three persons. In other words, the Godhead has forever been, is now, and will forever subsist as three persons. None of the persons came into being or became divine at a given moment in time.
Third, the three members of the Godhead are distinct persons and can be distinguished from each other (the Father is not the Son, the Father is not the Holy Spirit, and the Son is not the Holy Spirit). Orthodox Trinitarianism therefore rejects all forms of modalism (that blends or confounds the persons by defining them as mere modes of existence). God’s “oneness” and “threeness” are in different respects.
The one true God is revealed in three distinct but not separate persons.
To quote the ancient Athanasian Creed:
Thus the Father is God, the Son is God, the Holy Spirit is God. Yet there are not three gods; there is but one God.
For more on the historic Christian doctrine of the Trinity, see “How Can God Be Three and One?” in my book Without a Doubt: Answering the 20 Toughest Faith Questions.