An ordinance is a religious ritual whose intent is to demonstrate an adherent's faith. Examples include baptism and the Lord's Supper, as practiced in Evangelical churches adhering to the doctrine of the believers' Church, such as Anabaptists, all Baptist churches, Churches of Christ groups, and Pentecostal churches.
Roman Catholics, Eastern Orthodox, and many historic Protestant traditions (Anglicans, Lutherans, Presbyterians, Methodists, Moravians, and Reformed) prefer the use of the term "sacrament"
While a sacrament is seen as a means of grace from God, an ordinance is a practice that rather demonstrates the participants' faith. For example, some Christian traditions, such as Baptists, Churches of Christ, Christian Churches/Churches of Christ, Disciples of Christ, and Mennonites, do not call them "sacraments" because they believe these rituals are outward expressions of faith, rather than impartations of God's grace. The ordinances are often observed in remembrance of Jesus--primarily his baptism and the Last Supper (Holy Communion).
John Calvin and most other Protestant leaders rejected the Roman Catholic sacramental system but retained its vocabulary, applying the term "sacrament" only to ordinances instituted by God himself (cf. Westminster Confession of Faith 27; Belgic Confession 33). ... Unlike Baptists and Anabaptists, who tend to speak of baptism only as an "ordinance," Calvinists have characteristically spoken of baptism not only as an ordinance but also as a sacrament or a mystery, a rite through which God applies grace.
Christians agree universally that baptism and the Lord's Supper were instituted by Christ and should be observed as "ordinances" or "sacraments" by His followers.