Large language models (LLMs) are transforming medical artificial intelligence (AI) through three deployment paradigms. Text-only LLMs achieve near-expert performance on medical licensing benchmarks but cannot process images directly. Vision-language models (VLMs) enable radiology report generation, dermoscopic diagnosis, and fundus image grading through joint image-text representations, though at the cost of large annotated corpora and limited interpretability. Agentic LLMs employ a central model that orchestrates specialised external modules for segmentation, classification, and knowledge-graph reasoning, delivering superior modularity and auditability but introducing inference latency and orchestration complexity. We compare these paradigms across four medical domains (neuro-oncology, dermatology, ophthalmology, and cardiology) along eight dimensions. We conclude with a research agenda for hybrid architectures leveraging the complementary strengths of all three paradigms.