My understanding - centrism is a self-defining position that seeks to compromise between the perceived right and left (i.e. overton window shit, however much you believe in that). Radical centrism, if not used pejoratively, is the idea that these ideas shouldn't just be reached as a compromise, but should be pursued vigorously - a radical centrist in America today might demand police reform but also "fiscal responsibility." The Third Way is a specific project that attempts to merge left-ish social justice issues with a rejection of the Keynesian social democratic economic policy in the wake of the Nixon shock and the neoliberal project, adopted by Blairites in the UK and the Clintons (and by extension the Dems) in the US.