Cross-domain recommendation (CDR) has been proposed to alleviate the data sparsity issue in recommendation systems and has garnered substantial research interest. In recent years, dual-target CDR has been an increasingly prevalent research topic that emphasizes simultaneous enhancement in both the source and target domains. Many existing approaches rely on overlapping users as bridges between domains, yet in real-world scenarios, the number of such users is often severely limited, restricting their practical applicability. To overcome this limitation, alternative methods for cross-domain connections are needed, and item tags serve as a promising solution. However, real-world tags suffer from severe deficiencies in terms of both quantity and diversity, and existing studies have not fully exploited their potential. In this paper, we introduce Tag-Augmented Dual-Target Cross Domain Recommendation (TA-DTCDR), which is the first to apply LLM-distilled tag information to CDR. TA-DTCDR utilizes item tags distilled by large language models (LLMs) as an additional channel to facilitate information transfer, thereby mitigating performance decline caused by the lack of overlapping users. Furthermore, to fully leverage the natural language information carried by the distilled tags, we design a series of training tasks to align tag semantics across domains while preserving their semantic independence. The proposed method is validated on multiple tasks using public datasets, showing significant improvements over existing state-of-the-art approaches.