Wildfires present a significant threat to ecosystems and human life, requiring effective prevention and response strategies. Equally important is the study of post-fire damages, specifically burnt areas, which can provide valuable insights. This research focuses on the detection and classification of burnt areas and their severity using RGB and multispectral aerial imagery captured by an unmanned aerial vehicle. Datasets containing features computed from multispectral and/or RGB imagery were generated and used to train and optimize support vector machine (SVM) and random forest (RF) models. Hyperparameter tuning was performed to identify the best parameters for a pixel-based classification. The findings demonstrate the superiority of multispectral data for burnt area and burn severity classification with both RF and SVM models. While the RF model achieved a 95.5% overall accuracy for the burnt area classification using RGB data, the RGB models encountered challenges in distinguishing between mildly and severely burnt classes in the burn severity classification. However, the RF model incorporating mixed data (RGB and multispectral) achieved the highest accuracy of 96.59%. The outcomes of this study contribute to the understanding and practical implementation of machine learning techniques for assessing and managing burnt areas.