Different embedding models map inputs to incompatible vector spaces, forcing costly re-embedding when models are switched or combined. We present Relative Anchor Translation (RAT), a zero-shot protocol that translates between embedding spaces by comparing similarity profiles to shared anchor points, requiring no training data or learned parameters. Evaluating 17 models from 9 families—spanning BERT-family encoders, a decoder-based LLM, and a scale series from 22M to 335M parameters—we find that translation accuracy is governed by two continuous, independent factors: RDM correlation (ρ = 0.425 with R@1) captures shared representational structure, while similarity compression (ρ = −0.477) captures discriminability loss. All 17 models share structure to varying degrees; no binary boundary exists. RAT achieves Recall@1 from 0.2% to 99.6% across 272 directed pairs, with a crossover against linear alignment at K ≈ 100 anchors. We provide a practical decision protocol computable from anchor embeddings alone. Code: pip install rat-embed. Code and data: https://github.com/jiro-prog/rat-experiment Implementation was conducted using Claude Code (Anthropic). Experimental design, analysis, and manuscript drafting were assisted by Claude (Anthropic). The author takes full responsibility for all content.