By having "the gift of the Holy Spirit" in Acts 10:45 demonstrates these Gentiles had the indwelling of the Holy Spirit
before their water baptism (Acts 10:48).
"
The gift of the Holy Spirit" in Acts 2:38 and Acts 10:45 refers to the indwelling Holy Spirit
1. The same phrase
2. By the same author
3. In the same book
4. In the same context (the preaching of the Lordship and resurrection of Christ)
a. BDAG (3rd Edition): receive the Spirit as a gift
Ac. 2:38; cp. 10:45 (dōrea, page 266).
b. Thayer's Greek-English Lexicon of the New Testament: with an epexegetical gen. of the thing given, the Holy Ghost,
Ac 2:38,
10:45 (dōrea, page 161).
Doug believes Acts 2:38 refers to the indwelling of the Holy Spirit.
But then he (incorrectly) denies this is what is taking place in Acts 10:45. The two Greek lexicons quoted above associate both uses of "gift" in regards to the Holy Spirit. They do
not make a differentiation that Doug does.