Local Model
A model is "local" when it runs on infrastructure that a known, local entity owns or controls, rather than being accessed as a service on someone else's servers. Model locality says nothing on its own about the data a model was trained on. Local is not the same as small: small is about the model's size, local is about the infrastructure, and you can run a small model on a commercial cloud (not local) or a large model on your own hardware (local).
Locality is what most directly serves data sovereignty: a model run on a community's own infrastructure keeps language material and queries from ever leaving that environment, unlike a commercial closed-weight service.