This article addresses the issue of the contribution of SSE to the SDGs through a comparative analysis conducted in two countries: France and South Korea. The theoretical perspective adopted is that of public action renewal through a co-production process and the method uses a multidimensional analysis of the institutionalisation of SSE in both surveyed countries. Our results show that, far from a path dependency, there is a convergence process based on an increasing heterogeneity of the SSE dynamics in each of the national contexts. They also reveal that the institutionalisation of SSE reflects two conceptions of social innovation that each characterise the renewal of public action. In Korea, this conception is based on the production of goods and services with a social purpose by private actors, and in France, on co-construction processes that have been widely experimented with by SSE actors but remain unfinished. The result is an original and specific contribution in both countries to the SDGs, although this contribution is not fully explicit and recognised, both in terms of its results and process. This invisibilisation weakens the transformative potential of SSE in its contribution to sustainable development.