The “green new deal” appears to have several meanings. It has been used by mainstream neoliberal politicians to describe an investment program, operated completely through markets, that would shift the economy away from fossil fuels. The left-wing politicians you mention see the “green new deal” as a program of state infrastructure investment, a mobilization of resources on the scale of a war effort.
Whether such a war-type mobilization would ever be implemented in any significant capitalist country remains to be seen. The political scientists Geoff Mann and Joel Wainwright suggest in their book Climate Leviathan that there could be an international agreement between the US, China and others that would undertake such spending, but very much in the strongest countries’ neo-imperial interests, and with a big dose of geoengineering. Obviously the left politicians’ perspectives are quite different.