Maybe both are true.
The Greek word used in the bible for “believe” also covers the following:
Faith in
Trust in
Confidence in
So the Protestants have taken what was a rather encompassing word and said, well if you “believe” there Jesus you are saved. Ponder this the demons believe in Jesus, they know what he is, are they saved? Not bloody likely. The simple English definition is not sufficient to convey the full meaning and implication of the Greek word, in which the gospels were originally written.
http://www.biblehub.com/greek/4100.htm
Hint: Also recall Christ says you must approach him as a child would. What does that mean? Something to ponder.
The context, and I know that's a new concept for many Catholics on these threads, will determine how the word is to be understood.
4100 pisteúō (from 4102 /pístis, "faith," derived from 3982 /peíthō, "persuade, be persuaded") – believe (affirm, have confidence); used of persuading oneself (= human believing) and with the sacred significance of being persuaded by the Lord (= faith-believing). Only the context indicates whether 4100 /pisteúō ("believe") is self-serving (without sacred meaning), or the believing that leads to/proceeds from God's inbirthing of faith.
http://biblehub.com/greek/4100.htm
They are not saved because of that, not because of the issue of believing or not believing.
Here are some verses from Scripture that talk about believing and being saved, some the very words of Jesus Himself.
John 1:10-13 He was in the world, and the world was made through him, yet the world did not know him. He came to his own, and his own people did not receive him. But to all who did receive him, who believed in his name, he gave the right to become children of God, who were born, not of blood nor of the will of the flesh nor of the will of man, but of God.
John 3:14-18 And as Moses lifted up the serpent in the wilderness, so must the Son of Man be lifted up, that whoever believes in him may have eternal life. “For God so loved the world, that he gave his only Son, that whoever believes in him should not perish but have eternal life. For God did not send his Son into the world to condemn the world, but in order that the world might be saved through him. Whoever believes in him is not condemned, but whoever does not believe is condemned already, because he has not believed in the name of the only Son of God.
John 5:24 Truly, truly, I say to you, whoever hears my word and believes him who sent me has eternal life. He does not come into judgment, but has passed from death to life.
John 6:37-39 All that the Father gives me will come to me, and whoever comes to me I will never cast out. For I have come down from heaven, not to do my own will but the will of him who sent me. And this is the will of him who sent me, that I should lose nothing of all that he has given me, but raise it up on the last day.
John 6:40 For this is the will of my Father, that everyone who looks on the Son and believes in him should have eternal life, and I will raise him up on the last day.”
Romans 10:9-13 because, if you confess with your mouth that Jesus is Lord and believe in your heart that God raised him from the dead, you will be saved. For with the heart one believes and is justified, and with the mouth one confesses and is saved. For the Scripture says, “Everyone who believes in him will not be put to shame.” For there is no distinction between Jew and Greek; for the same Lord is Lord of all, bestowing his riches on all who call on him. For “everyone who calls on the name of the Lord will be saved.”
Acts 16:27-31 When the jailer woke and saw that the prison doors were open, he drew his sword and was about to kill himself, supposing that the prisoners had escaped. But Paul cried with a loud voice, “Do not harm yourself, for we are all here.” And the jailer called for lights and rushed in, and trembling with fear he fell down before Paul and Silas. Then he brought them out and said, “Sirs, what must I do to be saved?” And they said, “Believe in the Lord Jesus, and you will be saved, you and your household.”
Hint: Also recall Christ says you must approach him as a child would. What does that mean? Something to ponder.