It's three Persons in one Divine Nature, all separate in their personhood, all equal in their divinity. Am An image pulled from an old catechism diagrams the relationship like this:
The legendary analogy that Saint Patrick used when educating the Irish was the shamrock: three distinct leaves in one plant. Obviously, any image we make is going to be an imperfect representation of what the Trinity is, but the essence is that the three distinct persons are united in their shared Divine nature.