Purpose: This paper investigates both similarities and differences between two global threats represented by climate change (CC) and Covid-19 (CV). This will help understand the reasons behind the recognition of the CV as a pandemic that requires global efforts, whereas efforts to tackle climate change still lack such urgency. This paper aims to answer to the following questions: What are the elements that make CV restrictions acceptable by both the public and policymakers? and What are the elements that make CC restrictions not acceptable? Design/methodology/approach: This paper analyses the situation reports released by the World Health Organisation between the 11th of March (declaration of pandemic) and the 22nd of April, and their associated documents such as the Strategic Preparedness and Response Plan (WHO), the Risk Communication and Community Engagement Action Plan (WHO) and its updated version (WHO) and the Handbook for public health capacity-building (WHO). The analysis ends one week after President Trump’s announcement to suspend US funding to WHO (Fedor and Manson, 2020) and his support to public demonstrations against restrictions. Findings: The application of the second stage of the “Crisis and Emergency Risk Communication” model identifies five lessons that can be learned from this comparison. These relate to the necessity to simultaneously warn (about the severity of a threat) and reassure (by suggesting specific courses of action) the public; the need for multilevel collaboration that integrates collective and individual actions; the capacity to present cohesive messages to the public; the risk of politicisation and commodification of the issue that might undermine global efforts to tackle the threat; and the capacity to trigger individual responses through the promotion of self-efficacy. Originality/value: This paper identifies both similarities and differences between CC and CV managements to understand why the two threats are perceived and tackled in different ways. The analysis of official documents released by both the World Health Organisation and the Intergovernmental Panel on Climate CV outbreak as a crisis, whereas climate change is still anchored to the status of a future-oriented risk.