Here...
Romans 5:10-11
King James Version (KJV)
10 For if, when we were enemies, we were reconciled to God by the death of his Son, much more, being reconciled, we shall be saved by his life.
11 And not only so, but we also joy in God through our Lord Jesus Christ, by whom we have now received the atonement.
...the concepts combined and essentially made identical. I don't think we can separate Reconciliation and Atonement.
Secondly, we cannot compare the atonement of the Old Testament (obtained through animal sacrifice) with The Atonement, because men were not reconciled to God through those sacrifices.
The word
katallagē ("the atonement", reconciled is
katallassō)in v.11 is also translated reconciliation in the KJV:
Romans 11:15
King James Version (KJV)
15 For if the casting away of them be the reconciling of the world, what shall the receiving of them be, but life from the dead?
2 Corinthians 5:18
King James Version (KJV)
18 And all things are of God, who hath reconciled us to himself by Jesus Christ, and hath given to us the ministry of reconciliation;
Here, "hath reconciled" is again
katallassō. "Of reconciliation" is
katallagē.
2 Corinthians 5:19
King James Version (KJV)
19 To wit, that God was in Christ, reconciling the world unto himself, not imputing their trespasses unto them; and hath committed unto us the word of reconciliation.
"Reconciling" is
katallassō, "of reconciliation" is
katallagē.
Men do not receive Atonement until they are reconciled, which is what I think you are trying to say, if I am not mistaken. They are one and the same event. It happens at the time of salvation for each believer, the only exception being the Old Testament Saints who had died, who were reconciled to God, receiving Atonement that was not provided by animal sacrifice.
I would suggest it does, because we are dealing with the sum total of Christ's Work. Reconciliation was made possible through the Atonement.
Only in an Old Testament context. They did receive atonement and remission of sins...
Leviticus 4:20
King James Version (KJV)
20 And he shall do with the bullock as he did with the bullock for a sin offering, so shall he do with this: and the priest shall make an atonement for them, and it shall be forgiven them.
...but again that was a temporal and temporary atonement, pertaining to the flesh, or, physical in nature, like all Old Testament parables/shadows/figures/types.
The Writer of Hebrews makes it clear that the blood of bulls and goats could never take away sins, but the offering of Christ does, making one complete in regards to remission of sins forever.
A person cannot, in this Age, "be atoned for" by anything other than the Sacrifice of Christ.
Reconciliation is God's Work through Christ of bringing men into eternal union with Himself. This did not happpen in the Old Testament, for it was not until Christ appeared, died for our sin, returned to Heaven and sent the Comforter that He began to eternally indwell men. John 14 makes it clear that the Eternal Indwelling was yet a future event in the lives of men.
"At-One-ment" is precisely what Christ taught the disciples would happen:
John 14:15-18
King James Version (KJV)
15 If ye love me, keep my commandments.
16 And I will pray the Father, and he shall give you another Comforter, that he may abide with you for ever;
17 Even the Spirit of truth; whom the world cannot receive, because it seeth him not, neither knoweth him: but ye know him; for he dwelleth with you, and shall be in you.
18 I will not leave you comfortless: I will come to you.
22 Judas saith unto him, not Iscariot, Lord, how is it that thou wilt manifest thyself unto us, and not unto the world?
23 Jesus answered and said unto him, If a man love me, he will keep my words: and my Father will love him, and we will come unto him, and make our abode with him.
Remission of sins was the entire point of making atonement, both in the Old Testament and the New. What is different, though, is that when Atonement for sins is applied to us through salvation, it does not ever have to be repeated, because it is not temporal or temporary, but everlasting:
Hebrews 10:1-4
King James Version (KJV)
1 For the law having a shadow of good things to come, and not the very image of the things, can never with those sacrifices which they offered year by year continually make the comers thereunto perfect.
2 For then would they not have ceased to be offered? because that the worshippers once purged should have had no more conscience of sins.
3 But in those sacrifices there is a remembrance again made of sins every year.
4 For it is not possible that the blood of bulls and of goats should take away sins.
Hebrews 10:14
King James Version (KJV)
14 For by one offering he hath perfected for ever them that are sanctified.
God bless.