Short answers, pulled from the story.
The word martyr comes from the Koine Greek word mártys, which means witness or testimony. It was used in legal contexts for someone who speaks from personal observation, and Aristotle also used it for ethical judgments and expressions of moral conviction.
Stephen is the first martyr reported in the New Testament. He was accused of blasphemy and stoned by the Sanhedrin under Levitical law.
Pope Gregory I described three degrees in Homilia in Evangelia: red martyrdom for those who died by torture or violent persecution, white martyrdom for those such as desert hermits who pursued asceticism, and blue or green martyrdom for the denial of desires through fasting and penitent labor.
Tertullian, a second-century ecclesiastical writer, wrote that the blood of martyrs is the seed of the Church, arguing that a martyr's willing sacrifice leads to the conversion of others.
Scholars disagree. W. H. C. Frend argued that Christian martyrdom grew directly from Jewish roots, describing Judaism as a religion of martyrdom. G. W. Bowersock argued the opposite, that it emerged from the urban civic culture of the Roman Empire and was later borrowed by Jews. Daniel Boyarin challenged both, arguing the practice developed as Judaism and Christianity were still becoming distinct religions.
The distinction emerged in the latter part of the second century. Martyrs were only those who had suffered execution for their faith. Confessors were Christians who had endured imprisonment or torture and shown willingness to die, but had not been put to death. The Confessor of the Faith designation also applied to those who died in custody without being formally executed.