Conversion is the process by which a person decides to become Orthodox, as opposed to being brought up in the Orthodox faith from childhood. Such a person becomes an informal inquirer, then a formal catechumen before being brought into the church.
A convert, someone who has undergone conversion, may have any non-Orthodox background, including no religious beliefs (i.e., atheism), non-Christian religious beliefs (e.g., Muslim, Buddhist), or non-Orthodox or heterodox Christian beliefs (e.g. Roman Catholic, Protestant).
In the latter case, the individual may be received into the Church by the sacrament of chrismation, as long as the person has already had a baptism using the Trinitarian formula ("In the name of the Father, and of the Son, and of the Holy Spirit"). In the two former cases, individuals would be received by the sacrament of baptism, then chrismated.