Four words that are not synonyms
Self-hosted, on-premise, local and private each answer a different question, and marketing uses them interchangeably. Deciding which one you actually need is most of the requirements work.
Organisations that start from “it must be on-premise” often settle, once the data flows are drawn, for a single-tenant deployment with a defined model path, because that is what their obligations turn out to require.
- Self-hosted: the software runs on infrastructure you control, including your own cloud account. It says nothing about where the model runs.
- On-premise: your physical premises or data centre. Self-hosted software in your AWS account is not on-premise.
- Local model: the inference itself runs on hardware you control. This is what people usually mean by a private LLM.
- Private AI: the broadest term, covering single-tenant deployments and contractual data boundaries as well as fully local setups.