They were not saved "just by hearing Peter's words". They were saved when they were immersed in water, just like everyone else. If you read the context of Acts 10-11 thoroughly, you will see that they received the Holy Ghost (supernatural, immediate, personal indwelling) before they even had faith because it was as Peter began speaking, not after he had finished (Acts 11:15). So they hadn't even heard, hadn't believed, hadn't confessed, hadn't repented, had been immersed, yet received the Holy Ghost directly, without the laying on of the Apostle's hands. Why?
Acts 10:43
To him give all the prophets witness, that through his name whosoever believeth in him shall receive remission of sins. 44 While Peter yet spake these words, the Holy Ghost fell on all them which heard the word.
That tells me that the Holy Ghost fell on them that heard Peter's words. Note the reaction of the circumcision that believed for how & why they were astonished... that they had received the promise of the Holy Ghost as they had. And then Peter commanded them to be water baptized.
45 And they of the circumcision which believed were astonished, as many as came with Peter, because that on the Gentiles also was poured out the gift of the Holy Ghost. 46 For they heard them speak with tongues, and magnify God. Then answered Peter, 47 Can any man forbid water, that these should not be baptized, which have received the Holy Ghost as well as we? 48 And he commanded them to be baptized in the name of the Lord. Then prayed they him to tarry certain days.
To show that the choice to offer repentance and salvation to the Gentiles was God's idea, not man's. (Acts 10:45-47; Acts 11:18).
Romans 11:29 For the gifts and calling of God are without repentance.
Explain that as I see that to mean we cannot repent from all sins when we need him in us to do that in living as His in following Him. So the only repent I see to the Jews in Acts 2 was for what they were cut to the quick for; for crucifying Him Whom they had not believed and so to repent is to believe in Him.
Acts 2:
36 Therefore let all the house of Israel know assuredly, that God hath made the same Jesus, whom ye have crucified, both Lord and Christ. 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? 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. 39 For the promise is unto you, and to your children, and to all that are afar off, even as many as the Lord our God shall call.
It is a mistake to see the commandment to be water baptized as a means to receive the remission of sins for the Jews when the Gentiles received the remission for sins plainly without water baptism by believing in Him as clearly stated.
Are there 2 gospels? No. There is only one gospel and it is the same to the Jews as well as to the Gentiles; otherwise there can be no right hand of fellowship between Paul with James, John, and Cephas or Peter. Paul could not get in Peter's face for separating himself from gentile believers when the Jewish believers came in to fellowship when there is no difference between us.
Since the rest of your comments are based on a false premise, that I cannot explain, the arguments based on that false premise are also necessarily incorrect. However, I will respond nonetheless.
You assert this, but James clearly states in the immediate context that faith requires works to save (James 2:24) and that faith without works is dead (James 2:17). It's explicit, direct, unequivocal that faith alone, that is, faith without works is dead. Those who believe they are saved by faith alone believe they are, by definition, saved by a dead faith. Why? Because that's what faith alone is. Dead. If you believe you are saved by faith alone and faith alone is a dead faith, then you believe you are saved by a dead faith. There is no getting past this.
Try that again without reading it that salvation is by works.....
James 2:1My brethren, have not the faith of our Lord Jesus Christ, the Lord of glory, with respect of persons. 2 For if there come unto your assembly a man with a gold ring, in goodly apparel, and there come in also a poor man in vile raiment; 3 And ye have respect to him that weareth the gay clothing, and say unto him, Sit thou here in a good place; and say to the poor, Stand thou there, or sit here under my footstool: 4 Are ye not then partial in yourselves, and are become judges of evil thoughts? 5 Hearken,
my beloved brethren, Hath not God chosen the poor of this world rich in faith, and heirs of the kingdom which he hath promised to them that love him? 6 But ye have despised the poor. Do not rich men oppress you, and draw you before the judgment seats? 7 Do not they blaspheme that worthy name by the which ye are called? 8 If ye fulfil the royal law according to the scripture, Thou shalt love thy neighbour as thyself, ye do well: 9 But if ye have respect to persons, ye commit sin, and are convinced of the law as transgressors.
What is James saying here? That if you despise the poor and mistreat the poor, you are not saved? Why address these offenders as "my beloved brethren"? Why not simply say "You are false brethren. and thus not saved. Begone, heathen.!!!."? Is this about correction rather than judging who is saved from those that are not?
And James is not done rebuking the church for their mistreatment of the poor. James is now addressing how the church gets out of helping the poor after service by giving a benediction verbalizing their faith in God's Providence to the departing poor after church service,
James 2:14 What doth it profit, my brethren, though a man say he hath faith, and have not works? can faith save him?
Now the question arises; save who? Himself or someone else?
15 If a brother or sister be naked, and destitute of daily food, 16 And one of you say unto them, Depart in peace, be ye warmed and filled; notwithstanding ye give them not those things which are needful to the body; what doth it profit? 17 Even so faith, if it hath not works, is dead, being alone.
Someone else. The poor. So what faith is James rebuking? The church verbalizing their faith in God's Providence to the poor that God will provide for them just to get out of helping the poor from meeting their immediate needs. Note the end of verse 16 of the question; "
what doth it profit?" So what they say to the poor and yet give nothing to meet their immediate needs, what dos that profit the poor let alone save the poor from starvation and the elements when the church hardly leads by example in regards to their professed faith in His Providence.
18 Yea, a man may say, Thou hast faith, and I have works: shew me thy faith without thy works, and I will shew thee my faith by my works. 19 Thou believest that there is one God; thou doest well: the devils also believe, and tremble. 20 But wilt thou know, O vain man, that faith without works is dead? 21 Was not Abraham our father justified by works, when he had offered Isaac his son upon the altar? 22 Seest thou how faith wrought with his works, and by works was faith made perfect? 23 And the scripture was fulfilled which saith, Abraham believed God, and it was imputed unto him for righteousness: and he was called the Friend of God. 24 Ye see then how that by works a man is justified, and not by faith only.
Now James refer to that story that all Jews are well aware of .. or at least should be when God tempted Abraham to sacrifice his only son, Isaac. Hear what Abraham said to Isaac's question.
Genesis 22:7 And Isaac spake unto Abraham his father, and said, My father: and he said, Here am I, my son. And he said, Behold the fire and the wood: but where is the lamb for a burnt offering? 8 And Abraham said,
My son, God will provide himself a lamb for a burnt offering: so they went both of them together.
10 And Abraham stretched forth his hand, and took the knife to slay his son. 11 And the angel of the Lord called unto him out of heaven, and said, Abraham, Abraham: and he said, Here am I. 12 And he said, Lay not thine hand upon the lad, neither do thou any thing unto him: for now I know that thou fearest God, seeing thou hast not withheld thy son, thine only son from me. 13 And Abraham lifted up his eyes, and looked, and behold behind him a ram caught in a thicket by his horns: and Abraham went and took the ram, and offered him up for a burnt offering in the stead of his son.
14 And Abraham called the name of that place Jehovahjireh: as it is said to this day, In the mount of the Lord it shall be seen.
The meaning of the place is the moral of the story that the Lord will provide.
What Does It Mean that God Is Jehovah-Jireh?
So if a church verbalize their faith in God providing, then they should lead by example by meeting the immediate needs of the poor.
That faith in the Lord providing is not the same as that faith in Jesus Christ for salvation which is without works.