Whether the body tolerates a material vs. whether the material tolerates the body over time — two independent questions, not two names for one.
It's a natural assumption that a material safe enough to put in the body must also be a material built to last in the body — but nothing about being non-toxic implies durability. Biocompatibility asks a biological question: does the material provoke an adverse local or systemic response — inflammation, toxicity, an immune reaction — when it contacts tissue or blood? Biostability asks an entirely different, materials-science question: does the material resist chemical and mechanical degradation, corrosion, or dissolution over its intended service life in the body's aggressive physiological environment? A material can be biocompatible and biostable (titanium in a hip stem), biocompatible and deliberately not biostable (a resorbable suture), or — critically — biostable but not biocompatible (a durable material that nonetheless provokes a chronic adverse response).