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 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.
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" (Deuteronomy 6:5; Matthew 22:37).
"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). However, by Jesus' time, the Jewish leaders had made a religion out of God's desire to live in a love relationship with them (1 Timothy 1:8; Romans 7:12). Over the years, they had perverted God's Law into a works-based religion that alienated people from Him (Matthew 23:13–15; Luke 11:42). Then they added many of their own rules to make it even more cumbersome (Isaiah 29:13; Matthew 15:9). 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 (John 8:19). They had chosen religion over relationship.