Many studies show the advantages of direct current (DC) systems over alternating current (AC) systems for integrating renewable energy sources into the grid. However, protection design is still one of the key challenges, which delays the fast implementation of DC grids. High-voltage direct current (HVDC) is a well-established technology that resulted in several commercial installations. On the contrary, medium-voltage direct current (MVDC) is a technology in an earlier research and development stage with mostly research-based installations and only a few commercial ones. A research gap is present in many aspects of MVDC protection. This paper aims to review, compare and discuss the similarities and differences between HVDC and MVDC protection, and to propose potential strategies for future research and development in order to accelerate the development and integration of MVDC grid