NOT EXACTLY.
O.T. Saints are those that BELIEVED in their Hearts that MESSIAH WOULD COME, are SAVED BELIEVERS.
N.T. Saints ar e those that BELIEVED in their Hearts that MESSIAH DID COME, are SAVED BELIEVERS.
THAT IS THE EXACT SAME FAITH, the Faith of ABRAHAM.
So the 3000 that were converted to Christians the Day of Pentecost, were some of those very same O.T. SAINTS that became N.T. SAINTS.
I also believe that O.T. Saints will be the first to rise from there graves in the Resurrection:
1 Corinthians 15:22-23 (HCSB)
22 For as in Adam all die, so also in Christ all will be made alive.
23
But each in his own order: Christ, the firstfruits; afterward, at His coming, those who belong to Christ.
AND those Jews that had the same Faith as us, are Co-Equally part of the Bride of Christ, that will be called to Heaven for the Wedding of the Lamb. Here is the Proof:
Isaiah 54:5-6 (HCSB)
5
Indeed, your husband is your Maker— His name is Yahweh of Hosts— and the Holy One of Israel is your Redeemer; He is called the God of all the earth.
6
For the LORD has called you, like a wife deserted and wounded in spirit, a wife of one’s youth when she is rejected,” says your God.
Isaiah 62:5 (HCSB)
5 For
as a young man marries a young woman,
so your sons will marry you; and as a groom rejoices over ⌊his⌋ bride, so your God will rejoice over you.
They DEFINITELY are Part of the Bride of Christ.