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.
DeepSeek is an open-weight model family whose published training methods attracted attention for reaching competitive quality at lower reported cost. It solves the cost question in training rather than in inference, which is where most optimisation effort goes. It exists as evidence that architecture and training-schedule choices matter enough to change what a given budget can produce, and its weights and methods are published.