baptized in the name of Father Son and Holy spirit guaranty salvation, water baptism not.
Peter baptized Cornelius with water after Cornelius save. After his baptism with Holy spirit.
To confess/witnessing to public that now he is Jesus follower.
A Christian after save witnessing to other, but witnessing is not requirement for salvation. It is fruit of salvation. After save, abide to the vine, than branch will bear fruit. Not bear fruit for salvation, but bear fruit is product of salvation.
No body bear fruit before save, because branch can't bear fruit of itself.
It does not say Cornelius was saved after baptism of the Holy Spirit, you are reading that into it forcing it to say something it does not say and cannot prove.
There is one baptism for us:
Ephesians 4:5 (NKJV) one Lord, one faith, one baptism;
In Corinthians 10 we have two that are administered, however only one is able to save or Eph 4:5 is a lie.
In Matt 28:19 Jesus told all His disciples to "go baptize", he did not tell his disciples "go and I will baptize", He commanded a baptism that disciples can do to make disciples more disciples:
Matthew 28:19 (NKJV) Go therefore and make disciples of all the nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit,
You make "in the name of the Father and of the Son and of the Holy Spirit" some magical mystical confession, when what it is telling you is "do it as authorized by, the Father, Son and Holy Spirit", the ONLY authorized baptism is the one of Eph 4:5,
the one disciples are authorized to do (to think the Son needs authorization from the HS is silly)
There were 8 conversions in Acts, one was Cornelius, and he was the ONLY one recorded having been baptized by the HS, yet they like the other 7 were water baptized...
Peter knew that Cornelius required the water baptism of Eph 4:5, the one he and the others were commissioned and commanded (authorized) to do, so he water baptized them for remission of sins, the same authorized baptism in Acts 2:38, Peter commanded them to be water baptized in Acts 10:47.
Peter knew there was only one saving baptism, he knew Cornelius had just been baptized by our Lord, yet commanded them be baptized with water, why? because it is the baptism of Eph 4:5.
Nowhere does the scriptures ever say it was an act of obedience to "show" an inward faith, this is your man made doctrine and not the doctrine of Christ.