You and I live in a three-dimensional world. All physical objects have a certain height, width, and depth. One person can look like someone else, or behave like someone else, or even sound like someone else. But a person cannot actually be the same as another person. They are distinct individuals.
God, however, lives without the limitations of a three-dimensional universe. He is spirit. And he is infinitely more complex than we are.
That is why Jesus the Son can be different from the Father. And, yet the same.
The Bible clearly speaks of: God the Son, God the Father, and God the Holy Spirit. But emphasizes that there is only ONE God.
If we were to use math, it would not be, 1+1+1=3. It would be 1x1x1=1. God is a triune God.
Thus the term: “Tri” meaning three, and “Unity” meaning one, Tri+Unity = Trinity. It is a way of acknowledging what the Bible reveals to us about God, that God is yet three “Persons” who have the same essence of deity. Some have tried to give human illustrations for the Trinity, such as H2O being water, ice and steam (all different forms, but all are H2O). Another illustration would be the sun. From it we receive light, heat and radiation. Three distinct aspects, but only one sun.
No illustration is going to be perfect.
But from the very beginning we see God as a Trinity. Notice the plural pronouns “us” and “our” in Genesis 1:26 — Then God said, “Let us make man in our image, in our likeness, and let them rule over the fish of the sea and the birds of the air, over the livestock, over all the earth, and over all the creatures that move along the ground.”
Though not a complete list, here is some other Scripture that shows God is one, in Trinity:
“Hear, O Israel! The LORD is our God, the LORD is one!” (Deut. 6:4)
“I am the LORD, and there is no other; Besides Me there is no God.” (Isa. 45:5)
There is no God but one. (1Cor. 8:4)
And after being baptized, Jesus went up immediately from the water; and behold, the heavens were opened, and he saw the Spirit of God descending as a dove, and coming upon Him, and behold, a voice out of the heavens, saying, “This is My beloved Son, in whom I am well-pleased.” (Matt. 3:16-17)
“Go therefore and make disciples of all the nations, baptizing them in the name of the Father and the Son and the Holy Spirit.” (Matt. 28:19)
Jesus said: “I and the Father are one.” (John 10:30)
“He who has seen Me has seen the Father.” (John 14:9)
“He who beholds Me beholds the One who sent Me.” (John 12:45)
If anyone does not have the Spirit of Christ, he does not belong to Him. (Rom. 8:9)
“Joseph, son of David, do not be afraid to take Mary as your wife; for that which has been conceived in her is of the Holy Spirit.” (Matt. 1:20)
And the angel answered and said to her [Mary], “The Holy Spirit will come upon you, and the power of the Most High will overshadow you; and for that reason the holy offspring shall be called the Son of God.” (Luke 1:35)
[Jesus speaking to His disciples] “And I will ask the Father, and He will give you another Helper, that He may be with you forever; the Spirit of truth, whom the world cannot receive, because it does not behold Him or know Him, but you know Him because He abides with you, and will be in you.” … “If anyone loves Me, he will keep My word; and My Father will love him, and We will come to him, and make Our abode with him.” (John 14:16-17, 23)