Religion is man's attempt to please, or appease, God (or various gods or spirits) through prescribed actions or behavior. Ultimately, religion will always fail, because man is sinful and can never be perfect before a holy God.
Christianity, on the other hand, is placing one's faith and trust in the person of Jesus Christ. Rather than man trying to make himself acceptable to God, God has made the one who believes and trusts in Jesus acceptable to Himself, through the atoning work of the cross — that is, by forgiving his sins by the blood that was shed on the cross, and by placing man in right standing with God by virtue of his faith in Jesus. Thus man need not rely on his own faulty righteousness, which in God's sight is like filthy rags (Isaiah 64:6); instead, the perfect righteousness of Jesus Christ is imputed to the one who believes. (Romans 3:21-22, 4:5-6)