(HSRs) are human-made technologies that can take physical or digital form, resemble people in form or behavior to some degree, and are designed to interact with people. A common assumption is that social robots can and should mimic humans, such that human-robot interaction (HRI) closely resembles human-human (i.e., interpersonal) interaction. Research is often framed from the assumption that rules and theories that apply to interpersonal interaction should apply to HRI (e.g., the computers are social actors framework). Here, we challenge these assumptions and consider more deeply the relevance and applicability of our knowledge about personal relationships to relationships with social robots. First, we describe the typical characteristics of HSRs available to consumers currently, elaborating characteristics relevant to understanding social interactions with robots such as form anthropomorphism and behavioral anthropomorphism. We also consider common social affordances of modern HSRs (persistence, personalization, responsiveness, contingency, and conversational control) and how these align with human capacities and expectations. Next, we present predominant interpersonal theories whose primary claims are foundational to our understanding of human relationship development (social exchange theories, including resource theory, interdependence theory, equity theory, and social penetration theory). We consider whether interpersonal theories are viable frameworks for studying HRI and human-robot relationships given their theoretical assumptions and claims. We conclude by providing suggestions for researchers and designers, including alternatives to equating human-robot relationships to human-human relationships.