What does it mean that Jesus, Father, and Holy Spirit are of the same nature but different personas? To be clear right from the start: I have noted that some people do not believe in the doctrine of trinity, namely &quot;three personas, one nature&quot;, but my question is not about whether the doctrine is true! It is about understanding the doctrine. Thus this is not a question of opinion.

I have heard multiple times the doctrine that Jesus, Father, and Holy Spirit are personas of God or &quot;one God in three Divine persons&quot; (https://en.wikipedia.org/wiki/Trinity). According to Wikipedia:

The three persons are distinct, yet are one &quot;substance, essence or nature&quot;. In this context, a &quot;nature&quot; is what one is, whereas a &quot;person&quot; is who one is.

But what does this mean?
Sometimes it is compared with water also having three appearances, gas, liquid and ice, but I have been told that this is an example of Modalistic Monarchianism, which, as I have been told is a heresy according to one of the large early church councils. I do not have evidence for any of that because I am recalling from memory and are happy for corrections if I got something wrong. In any case, I see that for instance at the baptism of Christ, the Father, Son and Spirit are all distinctly present and interacting. So I see how this is not like water.
Quoting https://christiantoday.com.au/news/the-trinity-is-like-waterand-other-bad-analogies.html:

Other bad analogies
If water is inadequate, there are a wide array of alternative analogies we can turn to in modern theological parlance. Eggs are one, yet comprise yolk, shell and albumen. The sun comprises the sun itself, its light and its heat.
These are likewise erroneous or even heretical. Each part of the egg make up only one portion of the whole—the yolk is not the fullness of the egg. Yet the orthodox view is that each person of the Trinity is fully divine. Similarly, light and heat are simply creations of the sun, yet it is the heresy of Arianism to claim that the Son or Spirit are mere creations of the Father.

Ok, so I see what we do not mean when talking about the trinity. But what do we mean?
In that context I am not so much looking for a good analogy, but instead of a good explanation of the terms &quot;nature&quot; and &quot;person&quot; in the context of the trinity and in order to understand the trinity.
It seems to me that if those words cannot be defined properly, there is no point in using them in the first place, because that would be the same as stringing together syllables without meaning. In that case I would prefer to say &quot;Jesus, Father, Spirit are distinct and one at the same time and we don't know how that is possible.&quot; without introducing fancy words like &quot;nature&quot; or &quot;persona&quot;. To be honest, it actually sounds misleadingly similar to &quot;three gods&quot;, because a friend of mine and I also have the same &quot;nature&quot; of being human and are two different persons.
EDIT: I was asked to clarify what is unique of my question. In contrast to Are Father, Son, and Holy Spirit explicitly identified as &quot;persons&quot; in any writings directly associated with the Nicene Creed? I would like to get definitions of the words &quot;persona&quot; and &quot;nature&quot; and use these definitions to explain the term &quot;three personas, one nature&quot;.
Father, Son and Holy Spirit are one Deity. This is a matter of nature, just as we are one humanity.
But in our humanity we cannot (you and I) be a single humanity. Even if we be conjoined twins, there is only a partial unity.

But since God is Spirit and since 'fulness' is an attribute of divine nature, the persons of Deity are divinely one, in nature and form, in a perfection of union that is indivisible - one God.

See the First Council of Nicea. But some definitions are difficult to understand as they use terminology from outside of scripture or scriptural words (like 'hypostasis' and 'substance' and 'essence') which are not quite as scripture uses them.
What I have stated above ('unity', 'Spirit', 'fulness' and 'form' ) is in terms which are used in scripture.

I and my Father are one.[John 10:30 KJV]


God is Spirit [John 4:24, KJV]


For in him (Christ) dwelleth all the fulness of the Godhead bodily. [Colossians 2:9, KJV]


... being in the form, God ... [Philippians 2:6, KJV]