
The differences are difficult to explain but here is a great explanation from the Got Questions Ministries website (scriptures and bold type mine).
Question: "Is Christianity a religion or a relationship?"
Answer: Religion is “the belief in and worship of a superhuman controlling power, especially a personal God or gods.” In that respect, Christianity can be classified as a religion. However, practically speaking, Christianity has a key difference that separates it from other belief systems that are considered religions. That difference is relationship.
Most religion, theistic or otherwise, is man-centered. Any relationship with God is based on man’s works. A theistic religion, such as Judaism or Islam, holds to the belief in a supreme God or gods; while non-theistic religions, such as Buddhism and Hinduism, focus on metaphysical thought patterns and spiritual “energies.” But most religions are similar in that they are built upon the concept that man can reach a higher power or state of being through his own efforts. In most religions, man is the aggressor and the deity is the beneficiary of man’s efforts, sacrifices, or good deeds. Paradise, nirvana, or some higher state of being is man’s reward for his strict adherence to whatever tenets that religion prescribes.
In that regard, Christianity is not a religion; it is a relationship that God has established with His children. In Christianity, God is the aggressor and man is the beneficiary
Romans 8:3 (NLT)3 The law of Moses was unable to save us because of the weakness of our sinful nature. So God did what the law could not do. He sent his own Son in a body like the bodies we sinners have. And in that body God declared an end to sin’s control over us by giving his Son as a sacrifice for our sins.
The Bible states clearly that there is nothing man can do to make himself right with God
Isaiah 53:6 (NLT)6 All of us, like sheep, have strayed away. We have left God’s paths to follow our own. Yet the LORD laid on him the sins of us all.
Isaiah 64:6 (NLT)6 We are all infected and impure with sin. When we display our righteous deeds, they are nothing but filthy rags. Like autumn leaves, we wither and fall, and our sins sweep us away like the wind.
Romans 3:23-26 (NLT)23 For everyone has sinned; we all fall short of God’s glorious standard.
24 Yet God, with undeserved kindness, declares that we are righteous. He did this through Christ Jesus when he freed us from the penalty for our sins.25 For God presented Jesus as the sacrifice for sin. People are made right with God when they believe that Jesus sacrificed his life, shedding his blood. This sacrifice shows that God was being fair when he held back and did not punish those who sinned in times past,26 for he was looking ahead and including them in what he would do in this present time. God did this to demonstrate his righteousness, for he himself is fair and just, and he declares sinners to be right in his sight when they believe in Jesus.
Romans 6:23 (NLT)23 For the wages of sin is death, but the free gift of God is eternal life through Christ Jesus our Lord.
According to Christianity, God did for us what we cannot do for ourselves
Colossians 2:13 (NLT)13 You were dead because of your sins and because your sinful nature was not yet cut away. Then God made you alive with Christ, for he forgave all our sins.
2 Corinthians 5:21 (NLT)21 For God made Christ, who never sinned, to be the offering for our sin, so that we could be made right with God through Christ.
Our sin separates us from His presence, and sin must be punished
2 Thessalonians 1:7-9 (NLT)7 And God will provide rest for you who are being persecuted and also for us when the Lord Jesus appears from heaven. He will come with his mighty angels,
8 in flaming fire, bringing judgment on those who don’t know God and on those who refuse to obey the Good News of our Lord Jesus.9 They will be punished with eternal destruction, forever separated from the Lord and from his glorious power.
Isaiah 59:2 (NLT)2 It’s your sins that have cut you off from God. Because of your sins, he has turned away and will not listen anymore.
1 Peter 3:12 (NLT)12 The eyes of the Lord watch over those who do right, and his ears are open to their prayers. But the Lord turns his face against those who do evil.”

Ephesians 2:8-9 (NLT)8 God saved you by his grace when you believed. And you can’t take credit for this; it is a gift from God.9 Salvation is not a reward for the good things we have done, so none of us can boast about it.
2 Corinthians 5:21 (NLT)21 For God made Christ, who never sinned, to be the offering for our sin, so that we could be made right with God through Christ.
Grace is God’s blessing on the undeserving.
The grace-based relationship between God and man is the foundation of Christianity and the antithesis of religion. Established religion was one of the staunchest opponents of Jesus during His earthly ministry. When God gave His Law to the Israelites, His desire was that they “love the Lord your God with all your heart and with all your soul and with all your strength”
Matthew 22:37 (NLT)37 Jesus replied, “‘You must love the LORD your God with all your heart, all your soul, and all your mind.’
“Love” speaks of relationship.
Obedience to all the other commands had to stem from a love for God. We are able to love Him “because He first loved us”
1 John 4:19 (NLT)19 We love each other because he loved us first.
However, by Jesus’ time, the Jewish leaders had made a religion out of God’s desire to live in a love relationship with them.
Over the years, they had perverted God’s Law into a works-based religion that alienated people from Him.
Matthew 23:13 (NLT)13 “What sorrow awaits you teachers of religious law and you Pharisees. Hypocrites! For you shut the door of the Kingdom of Heaven in people’s faces. You won’t go in yourselves, and you don’t let others enter either.
Then they added many of their own rules to make it even more cumbersome.
Matthew 15:9 (NLT)9 Their worship is a farce, for they teach man-made ideas as commands from God.’”
They prided themselves on their ability to keep the Law—at least outwardly—and lorded their authority over the common people who could never keep such strenuous rules. The Pharisees, as adept as they were at rule-keeping, failed to recognize God Himself when He was standing right in front of them. They had chosen religion over relationship.
Just as the Jewish leaders made a religion out of a relationship with God, many people do the same with Christianity. Entire denominations have followed the way of the Pharisees in creating rules not found in Scripture. Some who profess to follow Christ are actually following man-made religion in the name of Jesus. While claiming to believe Scripture, they are often plagued with fear and doubt that they may not be good enough to earn salvation or that God will not accept them if they don’t perform to a certain standard. This is religion masquerading as Christianity, and it is one of Satan’s favorite tricks. Jesus addressed this in when He rebuked the Pharisees.
Matthew 23:1-7 (NLT)1 Then Jesus said to the crowds and to his disciples,2 “The teachers of religious law and the Pharisees are the official interpreters of the law of Moses.3 So practice and obey whatever they tell you, but don’t follow their example. For they don’t practice what they teach.4 They crush people with impossible religious demands and never lift a finger to ease the burden.5 “Everything they do is for show. On their arms they wear extra wide prayer boxes with Scripture verses inside, and they wear robes with extra long tassels.6 And they love to sit at the head table at banquets and in the seats of honor in the synagogues.7 They love to receive respectful greetings as they walk in the marketplaces, and to be called ‘Rabbi.’
Instead of pointing people to heaven, these religious leaders were keeping people out of the kingdom of God.
Holiness and obedience to Scripture are important, but they are evidences of a transformed heart, not a means to attain it.
God desires that we be holy as He is holy.
1 Peter 1:16 (NLT)16 For the Scriptures say, “You must be holy because I am holy.”
He wants us to grow in grace and knowledge of Him.
1 Peter 3:18 (NLT)18 Christ suffered for our sins once for all time. He never sinned, but he died for sinners to bring you safely home to God. He suffered physical death, but he was raised to life in the Spirit.
But we do these things because we are His children and want to be like Him, not in order to earn His love.
Christianity is about being born into the family of God.
John 3:3 (NLT)3 Jesus replied, “I tell you the truth, unless you are born again, you cannot see the Kingdom of God.”
It is a relationship.
Just as an adopted child has no power to create an adoption, we have no power to join the family of God by our own efforts. We can only accept His invitation to know Him as Father through adoption.
Ephesians 1:5 (NLT)5 God decided in advance to adopt us into his own family by bringing us to himself through Jesus Christ. This is what he wanted to do, and it gave him great pleasure.
Romans 8:15 (NLT)15 So you have not received a spirit that makes you fearful slaves. Instead, you received God’s Spirit when he adopted you as his own children. Now we call him, “Abba, Father.”
When we join His family through faith in the death and resurrection of Jesus, the Holy Spirit comes to live inside our hearts . He then empowers us to live like children of the King. He does not ask us to try to attain holiness by our own strength, as religion does. He asks that our old self be crucified with Him so that His power can live through us.
Galatians 2:20 (NLT)20 My old self has been crucified with Christ. It is no longer I who live, but Christ lives in me. So I live in this earthly body by trusting in the Son of God, who loved me and gave himself for me.
Romans 6:6 (NLT)6 We know that our old sinful selves were crucified with Christ so that sin might lose its power in our lives. We are no longer slaves to sin.
God wants us to know Him, to draw near to Him, to pray to Him, and love Him above everything. That is not religion; that is a relationship.
I’ll end with a quote from an anonymous source.
“The difference between Christianity and every other faith in the world is that all other religions are about man trying to reach up to God. Christianity is about God reaching down to man.”