Objection 1. It would seem that the limbo of hell is not the same as Abraham's bosom. For according to Augustine (Gen. ad lit. xxxiii): "I have not yet found Scripture mentioning hell in a favorable sense." Now Abraham's bosom is taken in a favorable sense, as Augustine goes on to say (Gen. ad lit. xxxiii): "Surely no one would be allowed to give an unfavorable signification to Abraham's bosom and the place of rest whither the godly poor man was carried by the angels." Therefore Abraham's bosom is not the same as the limbo of hell.
Objection 2. Further, those who are in hell see not God. Yet God is seen by those who are in Abraham's bosom, as may be gathered from Augustine (Confess. ix, 3) who, speaking of Nebridius, says: "Whatever that be, which is signified by thut bosom, there lives my Nebridius," and further on: "Now lays he not his ear to my mouth, but his spiritual mouth unto Thy fountain, and drinketh as much as he can receive wisdom in proportion to his thirst, endlessly happy." Therefore Abraham's bosom is not the same as the limbo of hell.
Objection 3. Further, the Church prays not that a man be taken to hell: and yet she prays that the angels may carry the departed soul to Abraham's bosom. Therefore it would seem that Abraham's bosom is not the same as limbo.
On the contrary, The place whither the beggar Lazarus was taken is called Abraham's bosom. Now he was taken to hell, for as a gloss [St. Gregory, Moral. xx] on Job 30:23, "Where a house is appointed for every one that liveth," says: "Hell was the house of all the living until the coming of Christ." Therefore Abraham's bosom is the same as limbo.
Further, Jacob said to his sons (Genesis 44:38): "You will bring down my grey hairs with sorrow to hell": wherefore Jacob knew that he would be taken to hell after his death. Therefore Abraham likewise was taken to hell after his death; and consequently Abraham's bosom would seem to be a part of hell.
I answer that, After death men's souls cannot find rest save by the merit of faith, because "he that cometh to God must believe" (Hebrews 11:6). Now the first example of faith was given to men in the person of Abraham, who was the first to sever himself from the body of unbelievers, and to receive a special sign of faith: for which reason "the place of rest given to men after death is called Abraham's bosom," as Augustine declares (Gen. ad lit. xii). But the souls of the saints have not at all times had the same rest after death; because, since Christ's coming they have had complete rest through enjoying the vision of God, whereas before Christ's coming they had rest through being exempt from punishment, but their desire was not set at rest by their attaining their end. Consequently the state of the saints before Christ's coming may be considered both as regards the rest it afforded, and thus it is called Abraham's bosom, and as regards its lack of rest, and thus it is called the limbo of hell. Accordingly, before Christ's coming the limbo of hell and Abraham's bosom were one place accidentally and not essentially: and consequently, nothing prevents Abraham's bosom from being after Christ's coming, and from being altogether distinct from limbo, since things that are one accidentally may be parted from one another.
Reply to Objection 1. The state of the holy Fathers as regards what was good in it was called Abraham's bosom, but as regards its deficiencies it was called hell. Accordingly, neither is Abraham's bosom taken in an unfavorable sense nor hell in a favorable sense, although in a way they are one.
Reply to Objection 2. The place of rest of the holy Fathers was called Abraham's bosom before as well as after Christ's coming, but in different ways. For since before Christ's coming the saints' rest had a lack of rest attached to it, it was called both hell and Abraham's bosom, wherefore God was not seen there. But since after the coming of Christ the saints' rest is complete through their seeing God, this rest is called Abraham's bosom, but not hell by any means. It is to this bosom of Abraham that the Church prays for the faithful to be brought. Hence the Reply to the Third Objection is evident: and the same meaning applies to a gloss on Luke 16:22, "It came to pass that the beggar died," etc., which says: "Abraham's bosom is the rest of the blessed poor, whose is the kingdom of heaven."
Source: Summa Theologica (New Advent)