A completely open model is one like the Allen Institute's Olmo model series:
The trained weights are open, the training software is open, and the data that goes into training the model is open.
Not many models are fully open.
An open weights model is one that has freely available trained weights, and maybe fine-tuning tools, but it lacks the original training data (and usually lacks the training software). These are the most commonly used local models, like Google's Gemma series, Meta's Llama, or Alibaba's Qwen.