LLM Gateway vs LLM Proxy vs LLM Router: What's the Difference?

Everyone calls their product a "gateway" now. LiteLLM markets itself as both a proxy and a gateway. Portkey is a gateway. Helicone's docs use proxy and gateway interchangeably. There's a well-cited Medium post by Bijit Ghosh that ranks on Google for this comparison — correct high-level definitions, but it stops before the implementation details that tell you what to actually choose and deploy. Here's the precise version: three different layers, concrete Go code for each, and a decision framewor...