These are my thoughts....
I think in reality, if we say "accepting Jesus", a few things happen at that moment.
God takes out our heart of stone and puts in us a new heart of flesh. This heart of flesh (not a hard stone anymore) can now accept Him as the Holy Spirit, who comes into the heart and dwells there. He puts godly fear into our new heart of flesh, so we will never go astray. Then everything else follows.
This is what happens to our heart when we accept Christ as Lord and Savior. The
circumcision of the heart.
No one is making up words to be said when accepting Christ as Savior. They are given to us in scripture. Here are few verses they are found in:
Romans 10
The word is near you, in your mouth and in your heart (that is, the word of faith which we preach): 9 that
if you confess with your mouth the Lord Jesus and believe in your heart that God has raised Him from the dead, you will be saved. 10 For
with the heart one believes unto righteousness, and with the mouth confession is made unto salvation. 11 For the Scripture says, Whoever believes on Him will not be put to shame. 12 For there is no distinction between Jew and Greek, for the same Lord over all is rich to all who call upon Him. 13 For
whoever calls on the name of the LORD shall be saved.
Acts 2
21 And it shall come to pass
That whoever calls on the name of the LORD
Shall be saved.
1 John 3
23 And this is His commandment:
that we should believe on the name of His Son Jesus Christ and love one another, as He gave us[e] commandment.
1 John 2
23 Whoever denies the Son does not have the Father either;
he who acknowledges the Son has the Father also.
1 John 5 (NKJV)
5
Whoever believes that Jesus is the Christ is born of God
1 John 4
2 By this you know the Spirit of God:
Every spirit that confesses that Jesus Christ has come in the flesh is of God, 3 and every spirit that does not confess that Jesus Christ has come in the flesh is not of God.
1 John 5
11 And this is the testimony: that God has given us eternal life, and this life is in His Son. 12 He who has the Son has life; he who does not have the Son of God does not have life. 13 These things I have written to you who believe in the name of the Son of God,
that you may know that you have eternal life, and that you may continue to believe in the name of the Son of God.
Matthew 16
16 Simon Peter answered and said,
You are the Christ, the Son of the living God. 17 Jesus answered and said to him, Blessed are you, Simon Bar-Jonah, for flesh and blood has not revealed this to you, but My Father who is in heaven.
scripture also tells us to repent - turn away from our old sinful way of life. As one grows in life with Christ they will turn away from more and more of the sin in their life. The old self dies away and is replaced by a new creation in Christ.
This will be noticeable in your life - by you, your friends, your relatives. You'll find that some you thought were friends will no longer be your friends. Some of your relatives won't like you much either.
If you don't see /live this change, you might want to revisit if you actually are saved. It doesn't result from some 'magic' words. It involves a heart change. A repentant heart.