Mistral is an open-weight model family that emphasises quality per parameter rather than raw size, so a small model can run on modest hardware without collapsing in quality. It solves the cost problem for teams whose workload is not hard enough to justify a frontier model. It exists because most production tasks are narrow enough that a well-trained small model is sufficient, and serving one is an order of magnitude cheaper than calling a large hosted model.
Gemma is a family of open-weight models from Google, published in sizes aimed at running on a single accelerator or a laptop. It solves the access problem for teams that want a capable model they can inspect and run themselves. It exists as the open counterpart to the hosted models, and its significance is that the weights are available for the smaller variants where local inference is realistic.