I don't know of any useful model that would match the usual definition of "open source". That is, where everything needed to build the thing is provided, such as the training data and code. Not that it would be tremendously useful anyways considering how expensive training a model is.

I much prefer the "open weights" term. It is not open source in the sense that you only get the finished product, not the actual source, but it is still open in the sense that it is not only accessible as a service.

For an analogy, take Quake for instance. When it was launched, its game server was available as an executable, so you could run it your machine, but that didn't make it open source. Only much later it was released as true open source software.