Cross-domain recommender systems have emerged, to address the cold-start problem and enhance recommendation outcomes by leveraging information transfer across different domains. Existing cross-domain recommender systems have investigated the learning of both domain-specific and domain-shared user preferences to enhance recommendation performance. However, these models typically allow the disparities between shared and distinct user preferences to emerge freely in any space, lacking sufficient constraints to identify differences between two domains and ensure that both domains are considered simultaneously. Canonical Correlation Analysis (CCA) has shown promise for transferring information between domains, by mapping their user representations into the same space. But, CCA only models domain similarities, and fails to capture the potential differences between user preferences in different domains. In this paper, we propose Discerning Canonical User Representation Learning for Cross-Domain Recommendation (DICUCDR), a generative adversarial networks (GAN) based method that learns both domain-shared and domain-specific user representations. DICUCDR introduces Discerning Canonical Correlation User Representation Learning (DCCRL), a novel design of non-linear Canonical Correlation mappings that creates a shared transformation for simultaneously mapping similarities between different domains and separating domain differences from domains. We compare DICUCDR against several state-of-the-art approaches using two real-world datasets. Our extensive experiments demonstrate the superiority of separately learning shared and specific user representations via DCCRL.