Social media have been the arena of different types of discourse during the COVID-19 pandemic. We aim to characterize public discourse during health crises in different international communities. Using Tweetpy and keywords related to the research, we collected 3,748,302 posts from the English, French, Portuguese, and Spanish Twitter communities related to two crises during the pandemic: (a) the AstraZeneca COVID-19 vaccine, and (b) the Omicron variant. In relation to AstraZeneca, ‘blood clot’ was the main focus of public discourse. Using quantitative classifications and natural language processing algorithms, results are obtained for each language. The English and French discourse focused more on “death”, and the most negative sentiment was generated by the French community. The Portuguese discourse was the only one to make a direct reference to a politician, the former Brazilian President Bolsonaro. In the Omicron crisis, the public discourse mainly focused on infection cases follow-up and the number of deaths, showing a closer public discourse to the actual risk. The public discourse during health crises might lead to different behaviours. While public discourse on AstraZeneca might contribute as a barrier for preventive measures by increasing vaccine hesitancy, the Omicron discourse could lead to more preventive behaviours by the public, such as the use of masks. This paper broadens the scope of crisis communication by revealing social media’s role in the constructs of public discourse.