The spread of COVID-19 misinformation on social media has become a major challenge for citizens, with negative real-life consequences. Prior research has focused on detection and/or analysis of COVID-19 misinformation. However, finer-grained classification of misinformation claims has been largely overlooked. The novel contribution of this paper is in introducing a fine-grained annotated misinformation dataset which distinguishes between statements that assert, comment or question on false COVID-19 claims. This new dataset not only enables social behaviour analysis but also enables us to address both an evidence-based and non-evidence-based misinformation classification. Lastly, through a ‘leave claim out’ validation, we demonstrate that classifier performance on unseen COVID-19 misinformation claims is significantly different, as compared to performance on topics present in the training data.