The shift to more sustainable sociotechnical systems is critical. The idea of the Circular Economy, although not completely new, has lately acquired prominence on policymakers' agendas to solve these and other environmental problems. While the words Circular Economy and sustainability are gaining popularity among academics, business, and politicians, the parallels and distinctions between the two ideas are still unclear. The connection between the ideas is not explicitly stated in the literature, which blurs their conceptual outlines and limits the effectiveness of applying the methods in study and practice. This study fills in the blanks, attempting to give conceptual clarity by differentiating words and synthesizing the many kinds of connections that exist between them. To examine the state of the art in the area and synthesize the similarities, differences, and connections between the two words, we performed a comprehensive literature review, using bibliometric analysis and snowballing methods. We found eight distinct kinds of relationships in the literature and drew the most obvious parallels and contrasts between the two ideas.