The design and application of LLM-based personas in AI companionship is a rapidly expanding but fragmented field, spanning from virtual emotional companions and game NPCs to embodied functional robots. This diversity in objectives, modality, and technical stacks creates an urgent need for a unified framework. To address this gap, this paper systematizes the field by proposing a Four-Quadrant Technical Taxonomy for AI companion applications. The framework is structured along two critical axes: Virtual vs. Embodied and Emotional Companionship vs. Functional Augmentation. Quadrant I (Virtual Companionship) explores virtual idols, romantic companions, and story characters, introducing a four-layer technical framework to analyze their challenges in maintaining long-term emotional consistency. Quadrant II (Functional Virtual Assistants) analyzes AI applications in work, gaming, and mental health, highlighting the shift from "feeling" to "thinking and acting" and pinpointing key technologies like enterprise RAG and on-device inference. Quadrants III & IV (Embodied Intelligence) shift from the virtual to the physical world, analyzing home robots and vertical-domain assistants, revealing core challenges in symbol grounding, data privacy, and ethical liability. This taxonomy provides not only a systematic map for researchers and developers to navigate the complex persona design space but also a basis for policymakers to identify and address the unique risks inherent in different application scenarios.