The aim of this paper is to offer an analysis of the notion of artificial moral agent (AMA) and of its impact on human beings’ self-understanding as moral agents. Firstly, I introduce the topic by presenting what I call the Continuity Approach. Its main claim holds that AMAs and human moral agents exhibit no significant qualitative difference and, therefore, should be considered homogeneous entities. Secondly, I focus on the consequences this approach leads to. In order to do this I take into consideration the work of Bostrom and Dietrich, who have radically assumed this viewpoint and thoroughly explored its implications. Thirdly, I present an alternative approach to AMAs—the Discontinuity Approach—which underscores an essential difference between human moral agents and AMAs by tackling the matter from another angle. In this section I concentrate on the work of Johnson and Bryson and I highlight the link between their claims and Heidegger’s and Jonas’s suggestions concerning the relationship between human beings and technological products. In conclusion I argue that, although the Continuity Approach turns out to be a necessary postulate to the machine ethics project, the Discontinuity Approach highlights a relevant distinction between AMAs and human moral agents. On this account, the Discontinuity Approach generates a clearer understanding of what AMAs are, of how we should face the moral issues they pose, and, finally, of the difference that separates machine ethics from moral philosophy.