In an attempt to differentiate sustainability finance, green finance and climate finance, I came across this excellent overview compiled by the European Political Strategy Center (EPSC, June 2017): Financing Sustainability Triggering Investments for the Clean Economy (pdf) which offers excellent illustrations.
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Illustrations as seen in above EPSC publication:
(3) Finance as motor for sustainable development
(4) Financial system
(5) Impacts of disasters on the economy