Self-Anchoring Calibration Drift (SACD), a tendency for large language models (LLMs) to show systematic changes in expressed confidence when building iteratively on their own prior outputs across multi-turn conversations. Through a controlled three-condition study comparing Claude Sonnet 4.6, Gemini 3.1 Pro, and GPT-5.2 across factual, technical, and open-ended domains, we find that SACD is real but multiform: models exhibit distinct self-anchoring signatures ranging from active confidence suppression to calibration improvement suppression, with effects concentrated in open-ended domains. These findings challenge the adequacy of single-turn calibration evaluation for characterizing LLM reliability in realistic multi-turn deployment contexts. Code and data are available at https://github.com/hvardhan878/calibration-drift