Carbon dioxide and hydrogen storage in geological formations at Gt scale are two promising strategies toward net-zero carbon emissions. To date, investigations into underground hydrogen storage (UHS) remain relatively limited in comparison to the more established knowledge body of underground carbon dioxide storage (UCS). Despite their analogous physical processes can be used for accelerating the advancements in UHS technology, the existing distinctions possibly may hinder direct applicability. This review therefore contributes to advancing our fundamental understanding on the key differences between UCS and UHS through multi-scale comparisons. These comparisons encompass key factors influencing underground gas storage, including storage media, trapping mechanisms, respective fluid properties, petrophysical properties, and injection scenarios. They provide guidance for the conversion of our existing knowledge from UCS to UHS, emphasizing the necessity of incorporating these factors relevant to their trapping and loss mechanisms. The article also outlines future directions to address the crucial knowledge gaps identified, aiming to enhance the utilisation of geological formations for hydrogen and carbon dioxide storage.