Catholic theology is precise: the distinctions between the persons of the Trinity lie not in their deity or in possession of divine attributes, but in their relations of origin—the Father is unbegotten, the Son is eternally begotten, and the Spirit proceeds from the Father (and, in Western theology, from the Son). What the Father is, the Son is, save only the property of paternity; what the Son is, the Father is, save only filiation.
Therefore they are two separate persons.
The Church teaches, in line with the Fathers and Councils, that the divine persons are distinct but not separate; they are not three gods, nor three beings, but one God in three persons.
One title, God, shared by 3 persons.