I wish I could remember the rest of the homily, because the distinction he drew wasn't immediately apparent to me either. Unfortunately, like many homilies, it did not stay in my head and so I can't explain the difference as my pastor explained it. But he definitely was defining the Catholic beliefs as different from "born again." I don't believe there is any such thing as a "born again Catholic."
Well, the phrase "born again" has a lot of baggage put on it by modern protestant churches. I presume that is the problem.
But call it "redemption" or "born again" the concept is --- in all Christian denominations --- that, by the death of Christ and accepting Him, the person is then a new creation (born again) without the baggage of original sin and as a slave to, well, the Devil. Of course, we promptly mess it up, but through repentence and the help of the Holy Spirit, one can be cleansed and the human nature to sin is slowly removed.
A non-instaneous process, alas.