Open-weights model
A model whose trained parameters are published, so anyone can run it on their own hardware — which is not the same as open source.
Published weights mean you can run the model locally, fine-tune it, and keep the data on your own machines. They do not mean you have the training data, the training code, or an unrestricted licence; many such models ship with terms that limit how they may be used.
The practical reason to reach for one is not price but control: an air-gapped machine, a regulated dataset, or a workload where a per-token bill does not fit. The practical cost is that you now operate a model — capacity, updates, and evaluation are yours.