Identifying disease interconnections through manual analysis of large-scale clinical data is labor-intensive, subjective, and prone to expert disagreement. While machine learning (ML) shows promise, three critical challenges remain: (1) selecting optimal methods from the vast ML landscape, (2) determining whether real-world clinical data (e.g., electronic health records, EHRs) or structured disease descriptions yield more reliable insights, (3) the lack of "ground truth," as some disease interconnections remain unexplored in medicine. Large language models (LLMs) demonstrate broad utility, yet they often lack specialized medical knowledge. To address these gaps, we conduct a systematic evaluation of seven approaches for uncovering disease relationships based on two data sources: (i) sequences of ICD-10 codes from MIMIC-IV EHRs and (ii) the full set of ICD-10 codes, both with and without textual descriptions. Our framework integrates the following: (i) a statistical co-occurrence analysis and a masked language modeling (MLM) approach using real clinical data; (ii) domain-specific BERT variants (Med-BERT and BioClinicalBERT); (iii) a general-purpose BERT and document retrieval; and (iv) four LLMs (Mistral, DeepSeek, Qwen, and YandexGPT). Our graph-based comparison of the obtained interconnection matrices shows that the LLM-based approach produces interconnections with the lowest diversity of ICD code connections to different diseases compared to other methods, including text-based and domain-based approaches. This suggests an important implication: LLMs have limited potential for discovering new interconnections. In the absence of ground truth databases for medical interconnections between ICD codes, our results constitute a valuable medical disease ontology that can serve as a foundational resource for future clinical research and artificial intelligence applications in healthcare.