More specifically, they are not one and same. Father is not Son is not Holy Spirit, but all of them are God.
Your questions are better answered by theologicians. I am not even a Christian, but even I know about concept of trinity. Perhaps everything about God is not meant to be comprehensible by humans. God is beyond humans after all.
For anyone wondering how this breaks down logically and where the error is:
The position as put here and elsewhere contains logical errors upon clarification. God has parts? Okay what makes the parts unique and discrete? If they aren’t, they aren’t parts of a whole and are equal to the whole.
For example: does the father have the same knowledge as the spirit? The same powers? If yes to these and similar questions, then they all are god and are not discrete. If no, then we don’t have one god at all, we have 3 gods. Also if no, the gods cannot be all knowing or all powerful individually.
I’ve never heard it put like this comment though. Instead I hear that they’re all god. As in, Jesus isn’t 1/3 of god, he is god. And so is the spirit/ghost and father. But if I ask if Jesus is the spirit, they’ll say no. This is an identity flaw. You’re saying that A=D and C=D but A!=C.
This is what you’re describing and is a good pictograph for explaining why it’s nonsense that cannot be presented in any accepted form of propositional logic.
OP commenter got mad at “pagans” for not describing something in terms of a contradictions, while accepting that contradiction on its own terms. Theist mad at accurate meme.
What’s so hard about it. My house is a home, a storage and an awful dump at the same time. All those have different attributes but they are the same house all together.
These are interchangeable, the trinity is not. Your house is/can be a home, storage, dump, but a home can be storage and storage can be a dump.
The claims of the trinity are that the son, father, and ghost are all god. But the ghost is not the son is not the father.
It’s an identity contradiction. A,B, and C all equal D. But A is not B is not C. The claim IS NOT A + B + C = D which would actually make sense and works with your analogy. Like yes my house is a dump + storage + home. That works. Does not work with the trinity.