Religion is the act of attempting to gain righteousness by accomplishing the works of the law in order to please God so that He might save you. This is self righteousness and it is impossible to attain and unacceptable before God.
Christianity is receiving the gift of righteousness by believing in Jesus Christ, the righteous one. Jesus fulfilled the law and all that God demanded and transferred His righteousness to one who believes in Him. This gift of righteousness received by faith in Jesus Christ is the only righteousness that is acceptable to God and determines the salvation of man.