Llama is a family of language models whose weights are published, so they can be run on your own hardware instead of only through an API. It solves the problem that most capable models are reachable only as a hosted service, which rules them out when data cannot leave your network or when per-token cost dominates. It exists because releasing weights turned out to build an ecosystem of fine-tunes and tooling around one architecture, and it is the model most local inference tools target first.
Qwen is an open-weight language model family from Alibaba, released in a range of sizes and with a strong showing on multilingual and code benchmarks. It solves the same problem as other open-weight models: letting a team run a capable model without depending on a closed API. It exists as one of the few families that publishes both very small and very large variants, which makes it a common default when you need a model that fits a specific memory budget.