This is classic speaking past one another. What you say is Protestant theology: a Christian is one who has been saved by a profession of faith, which means he is among the elect.
In Catholic theology, a Christian is one who has been baptised and did not commit an apostasy (e.g. became atheist or Muslim). At the end of everyone's life Christ judges him for his works and he either will be saved and go to heaven as one of the elect, or he will go to hell.
The judgement is based on the state of the soul at the point of death. A Christian who also obeyed the Church and repented of sin dies in the state of sanctifying grace and is saved. A Christian who dies burdened by sin and unreconciled is condemned. A non-Christian has no ordinary means of grace as he does not go to Church, and any such that are saved at all, are saved as an extraordinary expression of Christ's mercy.
This probably did not convince you to become Catholic, but it should help you understand what these words mean coming from a Catholic. In my experience, 90% of daily ecumenical bickering between Protestants and Catholics is simple lack of familiarity with the other side's terminology.
“In Catholic theology, a Christian is one who has been baptised”
See that’s where the Roman Catholic theology differs from what Paul said and practiced. In 1 Cor. 1:14-18, “I thank God that I baptized none of you, but Crispus and Gaius; Lest any should say that I had baptized in mine own name. And I baptized also the household of Stephanas: besides, I know not whether I baptized any other.
17 For Christ sent me not to baptize, but to preach the gospel: not with wisdom of words, lest the cross of Christ should be made of none effect. For the preaching of the cross is to them that perish foolishness; but unto us which are saved it is the power of God.”
Odd isn’t it that if baptism was necessary for salvation that Jesus would fail to commission Paul, an Apostle, to baptize.
So what you are saying is that a man could be very good his entire life, perform all the right acts, make all the right prayers, do everything his church demands of him, and in the last few seconds of his life commit a sin and die, and he will not go to heaven because he was not purified before he died?