No, that is not completely true. All our sins condemn us to Hell - unbelief is what sends us there.

Romans 6:23 For the wages of sin is death; but the gift of God is eternal life through Jesus Christ our Lord.

This includes the second death.

Ephesians 5:5-6 For this ye know, that no whoremonger, nor unclean person, nor covetous man, who is an idolater, hath any inheritance in the kingdom of Christ and of God. Let no man deceive you with vain words: for because of these things cometh the wrath of God upon the children of disobedience.

Revelation 21:8 But the fearful, and unbelieving, and the abominable, and murderers, and whoremongers, and sorcerers, and idolaters, and all liars, shall have their part in the lake which burneth with fire and brimstone: which is the second death.

1 Corinthians 6:9-11 Know ye not that the unrighteous shall not inherit the kingdom of God? Be not deceived: neither fornicators, nor idolaters, nor adulterers, nor effeminate, nor abusers of themselves with mankind, Nor thieves, nor covetous, nor drunkards, nor revilers, nor extortioners, shall inherit the kingdom of God. And such were some of you: but ye are washed, but ye are sanctified, but ye are justified in the name of the Lord Jesus, and by the Spirit of our God.