While "open weights" is probably the most appropriate terminology, and I do think a lot of AI companies have been abusing the term "open source", especially when releasing with restrictive community licenses (weights available w/ lots of restrictions is
very different than weights available under Apache 2.0/MIT), I think the binary talking point that's been getting popular lately is actually also pretty misleading.
Having open weights is a lot more useful than an exe/dll, especially with base models, as the weights are a lot more malleable. You can do continued pre-training or fine-tuning of models, basically being able to build on millions of dollars of free compute with as little as a few hours on a single gaming GPU. With the weights, you also get a lot more visibility into the model as well (which is getting more and more useful as more advanced interpretability research/tools become available). We've seen other white-box only techniques in the past, but the recent orthogonalization/abliteration one is wild: https://www.alignmentforum.org/posts/jGuXSZgv6qfdhMCuJ/refus... - other super-interesting stuff like model merges/evolutionary model merging are all things that can't happen without the weights.
There are of course really open models that include full data recipes, training logs, code, checkpoints, writeups, etc (LLM360 K2, AI2 OLMo are two recent ones) but there's a whole spectrum there, and honestly, there are very few "open" releases I've seen that aren't making at least some contributions back to the commons (often with gems in the technical reports, or in their code). Realistically, no one is re-running a training run to exactly replicate a model (from a cost, but also just a practical perspective - that model's already been trained!), but a lot of people are interested in tweaking the models to function better on their specific tasks (which actually lines up pretty well with the historical goals/impetus for open source - not to rewrite the whole code base, but to have the freedom to add the tweak you want).