At the first glance there seems to be an insignificant difference between the two terms. Looking a bit closer, the latter term is connected to spatial social innovation and is thus based on the spatiality of the social innovation concept. Social innovation initiatives are often rooted in the communities in which they take place and focus on addressing the needs of their community. In this sense, the space of social innovation is understood as the community in which the social innovation initiatives take place and that is affected by the outcome. Moulaert Frank and Mehmood Abid explain spaces of social innovation in chapter 18 of The Handbook of Local and Regional Development. In contrast, a space for social innovation is defined by its purpose: for social innovation. “For”, as a preposition (followed by a noun) means “intended to help or benefit someone/something”.
Thus, a space for social innovation is, in the most basic sense, a space that is intended to help or benefit social innovation, whereas a space of social innovation is the community in which social innovation initiatives take place and that benefits from them.