what is the difference between SON of GOD and son of God

is is common christian understand that their is a difference between the term SON (hyiós) of God and the other term son (teknon) of God -- these terms have different meaning and this is a fact .. but before we lay the case to rest .. we know an assertion does not hold weight, and there fore it is one thing to assert it, but to prove this is another thing altogether

and this is exactally what i will do using the bible to show the difference

For God so loved the world, that he gave his only Son (huios), that whoever believes in him should not perish but have eternal life. For God did not send his Son into the world to condemn the world, but in order that the world might be saved through him. Whoever believes in him is not condemned, but whoever does not believe is condemned already, because he has not believed in the name of the only Son of God -- john 3 :16 -18

But to all who did receive him, who believed in his name, he gave the right to become children of God (teknon theos), who were born, not of blood nor of the will of the flesh nor of the will of man, but of God. -- john 1 :13 -14 -----

in these two passages we see that john uses a different word to discribe who jesus is -- from that of an ordinary believer .. and these two word have very different meaning to them -- more on this later, as want to further establish this fact -- here we will look at some key passage from mark, matthew and from paul writings as well as hebrews

The beginning of the gospel of Jesus Christ, the Son ( huios) of God -- mark 1: 1

He said to them, “But who do you say that I am?” Simon Peter replied, “You are the Christ, the Son (huios) of the living God.-- matthew 16 :15 -16

and was declared to be the Son (huios) of God in power according to the Spirit of holiness by his resurrection from the dead, Jesus Christ our Lord -- romans 1 :4

Long ago, at many times and in many ways, God spoke to our fathers by the prophets, but in these last days he has spoken to us by his Son (huios), whom he appointed the heir of all things, through whom also he created the world --- hebrews 1 :1 -2

all the above text show that when the writers spoke of jesus they designated one specific word for who he was, and is ... being the uniques Son of God, who has always existed with the father .. this provides with a stronger testamony to our Lord and Saviour, the King of glory -- but as if this was not more to demonstate ... the term son (huios) has a very unique men and set of definitions .. that son (child of God does not carry

hyiós – properly, a son (by birth or adoption); (figuratively) anyone sharing the same nature as their Father. For the believer, becoming a son of God begins with being reborn (adopted) by the heavenly Father – through Christ (the work of the eternal Son). In the NT, 5207 /hyiós ("son") equally refers to female believers (Gal 3:28)

so when we consider what hebrews 1 says .. interms of the unique son we see that .. this term has a very unique triait or understnanding behind it ... which is "He is the radiance of the glory of God and the exact imprint of his nature"

so we have to understand this term being used of jesus proves his deity .. since it comes to mean that Jesus has the exact same nature .. he share the glory .. and perfect personafies what the father is like ... but he is not the father, he is the son

where as the term son of God in a believer case or child of God ... is teknon ... which has a very different meaning

téknon – properly, a child; (figuratively) anyone living in full dependence on the heavenly Father, i.e. fully (willingly) relying upon the Lord in glad submission. This prompts God to transform them into His likeness

téknon ("a child living in willing dependence") illustrates how we must all live in utter dependence upon the Lord (moment-by-moment), drawing guidance (care, nurture) from our heavenly Father. 5043 (téknon) emphasizes the childlike (not childish) attitude of heart that willingly (gladly) submits to the Father's plan. We profoundly learn this as we are receptive to Christ speaking His rhēma-word within to impart faith (cf. Ro 8:16,17 with Ro 10:17, Gk te

an example for us to get to would be

So then, brothers, we are debtors, not to the flesh, to live according to the flesh. For if you live according to the flesh you will die, but if by the Spirit you put to death the deeds of the body, you will live. For all who are led by the Spirit of God are sons of God. For you did not receive the spirit of slavery to fall back into fear, but you have received the Spirit of adoption as sons, by whom we cry, “Abba! Father!” The Spirit himself bears witness with our spirit that we are children (teknon) of God, and if children, then heirs—heirs of God and fellow heirs with Christ, provided we suffer with him in order that we may also be glorified with him. -- romans 8 :12 -17

so we see that christ unlike us has a totally different nature and the term emphasis' this fact .. but we are just adopted and the term is of ordinary use