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.
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.