There is no gospel of grace mentioned in Acts. The Jews who were under conviction did not asked what must we do to be saved? They asked what must we do in light of their murdering their messiah.
No this makes no sense in context to the preceeding events. They didn't have to ask what to do to be saved because it was known to all that, that was what the topic of the witnessing of the Apostles had been just before.
Look at the flow of what happened.
In Acts 2:4 The Apostles are filled with the Holy Spirit.
Act 2:4 And they were all filled with the Holy Ghost, and began to speak with other tongues, as the Spirit gave them utterance.
In Acts 2:21 the Apostles go out
witnessing about salvationAct 2:21 And it shall come to pass, that whosoever shall call on the name of the Lord shall be
saved.In Acts 2:37 the Jews were convicted in their hearts and asked what they should do.
Act 2:37 Now when they heard this, they were pricked in their heart, and said unto Peter and to the rest of the apostles, Men and brethren, what shall we do?
In Acts 2:38 the Apostles tell them to repent, be Baptized (calling on the name of the Lord) and receive the Holy Spirit.
Act 2:38 Then Peter said unto them, Repent, and be baptized every one of you in the name of Jesus Christ for the remission of sins, and ye shall receive the gift of the Holy Ghost.
In Acts 2:41 some of the Jews were baptized and added to the Church.
Act 2:41 Then they that gladly received his word were baptized: and the same day there were added unto them about three thousand souls.
So we have salvation, repentance, baptism, the Holy Spirit and membership in the Church mentioned all within one chapter, and that doesn't seem to you to be the Gospel of Grace?
Later in Acts 16:30,31 the jailer asked what must I do to be saved.
The Holy Spirit showed you the difference by the different wording,
No it doesn't use a different word. Saved is used in Acts 16:30-31 and it is used in Acts 2:21, same word both times.
Big difference.
No difference.