Baptism of the Spirit and indwelling of the Spirit, are they the same?

Why would anyone say that the baptism of the Spirit (apostles and Cornelius) and the indwelling of the Spirit are two different things. Just because one was manifested in signs does it make them different? If both are same, then Cornelius received the Spirit before he was baptized, hence saved. This would make baptism unnecessary for salvation. So those who say baptism is required have a need to differentiate between the two.
But do the scriptures differentiate between the two?

Lets go to Acts 2:33 - 'Therefore being exalted to the right hand of God, and having received from the Father the promise of the Holy Spirit, He poured out this which you now see and hear'.
Acts 2:39- "For the promise is to you and to your children, and to all who are afar off, as many as the Lord our God will call'
Both are talking about the promise of the Spirit as prophesied by Joel in Acts 2:17-21(in context). And the promise is to everyone.

Does everyone now have signs when they receive the Spirit? No. So it would only mean that both baptism of the Spirit and indwelling of the Spirit are the same. Also note that in Acts 10:17 Peter calls the Spirit as the gift of the Holy Spirit. So Peter doesnt differentiate between the gift of the Spirit and the promise of the Spirit. So why should we, unless we have a theory to push?

Read Galatians 3, where the promise is refered to the Spirit of Christ.