In the book of Acts, Luke uses 6-7 slightly different phrases when describing the "gift of the Holy Spirit." Is this significant?

Acts 1:8 sets the theme and tone for the book of Acts. God is doing something brand new in and through His people starting here after the resurrection and ascension of Jesus in regards to the Holy Spirit. He was giving His Spirit to His people in a different way.

In Acts 2, 4, 8, 10, and 19 we see different patters and orders of elements like preaching, baptism, the giving of the Holy Spirit, etc. Discussion can be had, but we must notice from every text that the Spirit of God in a Christian’s life does something.
- for some it comes with speaking in tongues (2:4; 10:46 ; 19:6)
- the gift of prophecy (2:17 ; 19:6; 10:46 )
- an overflowing praise of God's greatness (2:11 ; 10:46 )
- obedience to the commands of God (5:32 )
- courage and boldness to witness (2:14 –36; 9:17 –22)
- the working of various signs and wonders (6:8)

Jesus promises that when the Spirit comes upon a believer (every believer), they will receive power not to speak in tongues or prophecy, but to effectively witness for Him.

In Acts the testimony of Jesus is of utmost importance.
How we live and witness to Christ matters, just like what we proclaim about Him matters. And the Spirit leads us to places and people that we might not expect.