Accurate classification of cloud species and varieties is essential for meteorological observation and climate research, yet automated systems utilizing artificial neural networks to address the full World Meteorological Organization (WMO) taxonomy – including 14 species and 9 varieties – remain largely unexplored. Building upon our previous work on cloud genera classification, this study extends that foundation to address the finer taxonomic levels of species and varieties. We present an artificial neural network-based framework evaluated on ground-based images collected across Poland by over 50 experts from the PSHM IMGW-PIB network (2021–2026). Both Convolutional Neural Networks (CNNs) and Vision Transformer (ViT) architectures were evaluated. Multi-class species classification achieved F1 scores ranging from 49% to 79%. Notably, applying a hierarchical approach utilizing genera-specific models – leveraging our earlier findings – yielded improvements exceeding 19 percentage points for certain species. Classification accuracy followed a logarithmic trend with dataset size, where Transformer-based models outperformed CNNs for larger training datasets, while CNNs exhibited an advantage with smaller sample sizes. These findings demonstrate that neural network architectures can effectively classify cloud species and varieties, and that genera-level model stratification significantly enhances classification capability, suggesting potential for integration into operational meteorological workflows.