There are three leaves that are unique and distinct while the three still make up one clover. 4 - Water can exist in 3 phases, solid, liquid and steam. Ice is water. Steam is water. All of these analogies fall short at one point or another.
Lets see how.
God would be like the the Sun, the heat would be like the Holy Spirit, and the sunlight would be the Son. All these three help make up the sun. Yet the sun is not the sunlight itself. It is possible for light and heat to make up the sun, and not be identical to each other. Just like the members of the Godhead, not being identical to each other.