I agree with you that there is no difference. I suppose it's unfortunate the KJV translators used different words to translate one Greek word. In the original preface to their translation, which is almost never included in KJVs today, they note that they felt no need to use only one English word for each Greek (or Hebrew) word.
The experience of Cornelius and those with him, I believe, shows that people can be forgiven before being baptized. In
Acts 15, Peter is arguing against those Jewish believers who were saying that Gentile believers had to be circumcised to be saved, and he uses Cornelius's experience to show that God had fully accepted the Gentiles, as Gentiles, just as much as he had accepted the Jews, and what proved this was him pouring out the Spirit upon them.
In 15.8-9, Peter says, "8 And God, who knows the heart, bore witness to them, by giving them the Holy Spirit just as he did to us, 9 and he made no distinction between us and them, having cleansed their hearts by faith."
What showed that God had made no distinction between them and Jewish believers and that he had cleansed their hearts by faith was him giving them the Spirit. What would their hearts be cleansed of but their sins? This occurred before they were baptized.
I agree with you that, in the Book of Acts, Cornelius's experience of receiving the Spirit before baptism is the exception to the rule. And so, normally baptism is the place where someone is forgiven, but I think that Cornelius's experience shows that God can forgive apart from baptism in circumstances like his.
I would add that, when we receive the Spirit in conversion, the Spirit sanctifies us, that is, makes us holy and sets us apart for relationship with God. For example, Paul says in
2 Thess 2.13, "But we ought always to give thanks to God for you, brothers beloved by the Lord, because God chose you as the firstfruits to be saved, through sanctification by the Spirit and belief in the truth."
How could the Spirit's sanctifying work, his making us holy work, not include the removal of our sin?