"Open Source" is mostly the right term. AI isn't code, so there's no source code to open up. If you provide the dataset you trained off of, and open up the code used to train the model, that's pretty close.
Otherwise, we need to consider "open weights" and "free use" to be more accurate terms.
For example, ChatGPT 3+ in undeniably closed/proprietary. You can't download the model and run it on your own hardware. The dataset used to train it is a trade secret. You have to agree to all of OpenAI's terms to use it.
LLaMa is way more open. The dataset is largely known (though no public master copy exists). The code used to train is open source. You can download the model for local use, and train new models based off of the weights of the base model. The license allows all of this.
It's just not a 1:1 equivalent to open source software. It's basically the equivalent of royalty free media, but with big collections of conceptual weights.