The language of catechesis may be unfamiliar, but it’s a time-honored word, and worth recovering. It’s a biblical and historically rich word, and carries with it an important set of assumptions about Christian formation, which marks it out as a peculiar form of instruction or religious education. As a way of introduction, it may be helpful to know how various derivations of the word are used, as they often take on different shades of meaning.
Catechesis is a noun referring to the general art of instructing new believers in the faith, with a view towards comprehensive instruction in the basic tenants of belief, spirituality, and ethics.
A catechist is someone who does this teaching, while a catechumen is one who is taught—a “hearer.” In the early church, catechumen entailed a particular status in the church. They were not considered a pagan or outsider, but neither were they full members—they were not yet baptized, and could not participate in the Eucharist.
To catechize is the verb form referring to this kind of teaching, while catechetical is the adjectival form.
Catechetics is a way of describing the study of catechesis—similar to the way homiletics refers to the art of preaching.
The catechumenate is a term that refers to a process or period of time devoted to the instruction of new Christians. While this specific term wasn't used in the early church, the concept started to emerge. In the early church, one could be a catechumen anywhere from one to three years. By the fourth century, the catechumenate concluded with an intense time of training during the season of Lent, just before Easter when baptisms took place.
By the late Middle Ages and early Reformation period (late fifteenth, early sixteenth century), the term catechism emerged, usually in reference to a text in a question-and-answer format that those preparing for baptism would memorize and be tested on. In general it refers to the content of catechesis—what is taught.
During the Reformation, a number of catechisms appeared: Martin Luther wrote a Small and Large Catechism, Calvin wrote a Genevan Catechism, which underwent several editions, and later Reformed churches developed the Heidelberg Catechism, the large and small Westminster Catechisms, and several others. The Roman Catholic Church formulated its primary catechism during the Council of Trent at the end of the sixteenth century, and has since produced variations in local languages, the most recent being the English-language Catechism of the Catholic Church, published in 1992.
The difference between a catechism and a confession is that whereas a confession simply states a denomination’s doctrinal emphases, a catechism is typically presented in a question-and-answer format, and was designed especially for teaching and memorization. In the centuries following the Reformation, many Protestant pastors and theologians wrote catechisms in order to teach their flocks the basics of the faith, adapted to their particular circumstances and what was deemed most pressing.
 A similar set of definitions can be found in J. I. Packer and Gary Parrett, Grounded in the Gospel: Building Believers the Old-Fashioned Way (Downer’s Grove, IL: IVP Academic, 2010), 27–28.