Trust represents a key issue in building successful customer-supplier relationships. In this sense, social software represents a powerful means for fostering trust by establishing a direct, more personal communication channel with customers. Therefore, companies are now investing in social media for building their social digital brand and strengthening relationships with their customers. In this paper, we presented two experiments by means of which we investigated the role of traditional websites and social media in trust building along the cognitive and affective dimensions. We hypothesize that traditional websites (content-oriented) and social media (interaction-oriented) may have a different effect on trust building in customer-supplier relationships, based on the first impression provided to potential customers. Although additional research is still needed, our findings add to the existing body of evidence that both cognitive and affective trust can be successfully fostered through online presence. Specifically, social media provide companies with tools to communicate benevolence to potential customer and, therefore, foster the affective commitment of customers. Traditional websites, instead, are more appropriate for communicating the competence and reliability of a company, by fostering trust building along the cognitive dimension. The results of our studies provide implications for researchers and practitioners, by highlighting the importance of combining the two media for effectively building a trustworthy online company image.