What is the difference between Son of God and Son of Man?
Son of God.
Jesus is described as the only begotten Son of God. This comes from the Old Testament as it is written,
Ps 2:7 I will declare the decree: the LORD hath said unto me, Thou art my Son; this day have I begotten thee.
The word Son of God has to do with the deity of Christ. He is truly God. The relationship between the Father and the Son must be understood in a figurative sense. The word Son in our own human description has to do with the identity of nature and mutual affection. The only begotten Son means the only person in relation to the Father. Christ Jesus is the same nature with his Father that he is God. There is no inferiority in the Son as the Son is the Messiah and the Messiah has no inferiority. The Messiah is with the same nature with the Father, the Messiah and the Father are in some respect distinct from each other. The Father is not the Son and the Son is not the Father but they are one in divine nature, the Father and the Son are one. Also there is a mutual affection between them. Just like a father loves his son, if he has only one son. In the same way the Father loves the Son.
Also the Messiah is described as the Son of Man. It is a borrowed term from the Old Testament.
Ps 8:4 What is man, that thou art mindful of him? and the son of man, that thou visitest him?
Ps 80:17 Let thy hand be upon the man of thy right hand, upon the son of man whom thou madest strong for thyself.
The word Son of Man has to do with his humanity. God becoming a man. He is truly a man. At the same time distinguished from all other men. He is the perfect man. He is the one who represent his people to the Father. The second Adam. The God-man. God manifest in the flesh.