According to Acts 10:2, Cornelius feared God, but he was not converted yet. Cornelius wasn't converted until he heard the gospel from Peter. How was Cornelius's fear of God in Acts 10:2 different from a converted person's fear of God?
For someone who is not converted, their fear of God (if any) is just dread of punishment. There's no fearing God in the sense a child fears sinning against his loving father, but a criminal who's angered the judge.
1 John 4:18-19
"There is no fear in love, but perfect love casts out fear. For fear has to do with punishment, and whoever fears has not been perfected in love. We love because he first loved us."
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!”
I think the issue of conversion is secondary in Acts 10 and 11. Cornelius has the privilege of living in that intersection in time where Christ had accomplished redemption, and the outpouring of the Spirit was to testify that Jesus was the Christ by confirming the words of the apostles through power. The Spirit by the same act makes it indisputable that salvation is for the Gentiles as well as Jews so that there would be no prejudice against believing Gentiles.
Cornelius was already a Gentile believer with true faith in God (In my humble opinion) but had not become a full Jew i.e. circumcision, food laws, etc. Such people were called God-fearers of the Gentiles.
For example, when he went to worship at the Temple he would have been restricted to the Court of the Gentiles, because that "mid wall of partition" between Jewish and Gentile believers was only taken down in Christ (Ephesians 2).
Under the OT administration Gentile believers were somewhat "second class citizens".
When the Spirit of God, given at Pentecost, came upon Cornelius and his household, it was God's testimony that the NT Gospel and promise of the Spirit from the ascended Christ was for "unclean" Gentiles as well as "kosher" Jews. Although Christ had commanded them to go into all the world, Peter and the others had a lot of unbelief in this regard.
In the NT that wall is taken down and Gentile and Jewish believers have ceremonial and spiritual equality in Christ as part of the commonwealth of Israel and Israel of God (Gal 6:16), the trans-national and trans-historical people of God, the NT Church.
I might add another point. The angel said Cornelius alms have risen as a memorial to God.
Somehow God had already been working in Cornelius life in a god glorifying manner
Grace was already underway
Acts 10: 3 About the ninth hour of the day[a] he saw clearly in a vision an angel of God come in and say to him, “Cornelius.” 4 And he stared at him in terror and said, “What is it, Lord?” And he said to him, “Your prayers and your alms have ascended as a memorial before God.
Cornelius was converted. Can someone be regenerate without being converted? i.e. having some sense of his sinnership, faith in Christ and repentance towards God. Are good works acceptable to God, except in Christ?
Now, until Peter brought the Gospel message to him in its NT form, Cornelius would have had faith in Christ by means of types, ceremonies and prophecies.
We have many other examples in the NT of "OT faith" being transfigured into "NT faith", the substance of both being the same e.g. Simeon, Anna, Nathanael, the centurion with the sick servant, etc.
FF Bruce says that 'God fearers' is not a 'technical term' but a convenient one. These 'God fearers' were not ready to become card carrying Jews, but were dissatisfied by the polytheism of the day, and attracted to the monotheistic religion of the Jews and their way of life. They usually attended the local synagogue and were exposed to parts of the Word of God. The term 'God fearers' did not include the idea of conversion, for the Jews were not concerned with conversion, but circumcision. In other words,, all that the term 'God fearer' tells us is that Cornelius was NOT circumcised. Whether or not he was converted would have to be decided by other parts of the text.