According to Trinitarians, how does the one nature of God define what God is, while the three persons define who God is?

I've come across several instances of the Trinitarian explanation that God's one nature (or essence) defines **what** God is, while the three persons—Father, Son, and Holy Spirit—define **who** God is. For [example](https://relevantradio.com/2022/10/explaining-the-trinity-nature-and-person/) : > ... To wrap our heads around the Trinity, we have to distinguish the word “nature” from the word “person”. Our nature would be what suggests to us that there is a person, but the person is what possesses the nature. A person could not exist without his or her nature but ultimately, the person possesses their nature. > > Patrick applied this to Frank, his caller. Frank’s person tells us *who* he is. He is Frank and that is his person. Frank’s nature tells us *what* he is. He is a human being with a soul, intellect, and free will. Therefore, he has a human nature. When Jesus became incarnate, He had two natures, one human and one divine. He never ceased being God the Son. I’d like to understand more precisely how this distinction is made within Trinitarian theology. I’m particularly interested in how this is supported by both scripture and the historical teachings of the Church. For example, the **Fourth Lateran Council (1215)** declared: >"For there is one person of the Father, another of the Son, and another of the Holy Spirit: but the Godhead of the Father, Son, and Holy Spirit is one, their glory equal, their majesty coeternal." This seems to affirm the distinction between person (who) and essence (what), but I’d like help unpacking it more fully. How do Trinitarian theologians interpret this distinction, and how does it help preserve both monotheism and the full divinity of each person? I’m looking for answers from a classical Trinitarian perspective, whether Western (Catholic/Protestant) or Eastern Orthodox, and would appreciate scriptural, conciliar, or patristic sources that explore this topic.