In the global pursuit of sustainability, the role of private sector capital is pivotal, necessitating a shift in financial flows towards sustainable initiatives. However, the proliferation of greenwashing undermines trust among investors and consumers alike. The detection and mitigation of greenwashing demand robust automated systems. Nonetheless, this endeavor is challenging due to ambiguous definitions, limited availability of high-quality data, and the qualitative nature of sustainability claims. In contrast, the field of fake news detection, facing similar obstacles, has undergone substantial methodological evolution. Employing a systematic mapping approach, we link existing types of greenwashing and fake news, unveiling similarities and distinctions. Our findings contribute to the linking of these two fields by establishing the conceptual foundation to transfer methodological advancements, such as detection algorithms, from fake news literature to the realm of greenwashing. Furthermore, we outline promising research avenues in the domains of greenwashing, fake news and their intersection.