I'm Southern Baptist & this is indeed what we believe. We get that term from this Scripture:
John 3
Jesus Teaches Nicodemus
1Now there was a man of the Pharisees named Nicodemus, a member of the Jewish ruling council. 2He came to Jesus at night and said, "Rabbi, we know you are a teacher who has come from God. For no one could perform the miraculous signs you are doing if God were not with him."
3In reply Jesus declared, "I tell you the truth, no one can see the kingdom of God unless he is born again." 5"no one can enter the kingdom of God unless he is born of water and the Spirit. 6Flesh gives birth to flesh, but the Spirit gives birth to spirit.
Yes, we do believe that there is that moment when a person makes a conscience decision, but the Scripture also encourages us to "work out your salvation" (do good works, strive for spiritual maturity), hence, "being saved." We also believe that we "will be saved" from God's Wrath. Where we differ from Catholics (and others) is, we believe the individual must "choose" Jesus.