Yes, Jesus Christ is God the Son. However, God is trinitarian in nature, and you're likely referring to God the Father in the first part of your question, so the answer is no. Does that make things a bit clearer?
Jesus is God's son, firstborn of all creation, and the master worker by which he created all other things. The Almighty God's name is Jehovah, and Psalms 90:2 says that he has existed from times indefinite, whereas Colossians 1:15 says that Jesus was created. They are one in the sense that a husband and wife are "one", in purpose, spiritually. Jesus always referred to his "Father" in heaven, said that no one knew the end except for his Father, also said the Father was greater, and he prayed to his Father. Now, what sense does it make to say that they are the same, God the Son, God the Father, God the Holy Spirit, as the trinity doctrine states?
A "theological" statement: There are 3 persons in God. The Father, the Word, and the Holy Spirit. ( Through Generation & Spiration respectively) They have the same nature (divine). The Word "became flesh" (took on human nature) and "dwelt among us." (One person, two natures---AKA Jesus, the Christ.)
Jesus Christ is the Word made flesh. He is both God and Man. Yes, it is difficult to grasp. (Read "Theology and Sanity" by F.J. Sheed.)
Jesus is the human incarnation of God Himself - God in the flesh. To say Jesus is God means that He is a divine person, the Second Person of the Trinity, and that He possesses the divine nature: He acts as God acts (Jn 1:1, 20:28; Col. 1:15 2:9). To say He is the Son of God means that He is the Son of the Father, the First Person of the Trinity, and that He possesses the same divine nature as the Father (Mt 3:16-17; Heb 1:1-3). Perhaps this analogy will help: As a human being, you are the child of human parents, not mere animal parents. You possess a human nature from them. Well, Jesus is the eternal Son of the Father. He existed for all eternity with the Father as the divine Son before assuming a human nature and being born in Bethlehem two thousand years ago. He has existed for all eternity with the Father, eternally proceeding from Him as light streams forth from the sun (Jn 1:1-5). (My answer continues in the comments)