Earlier quoted context omitted.
What is an untrained model? That doesn't make sense. Do you mean the training code or just base models (even those are trained).
Alright, what's the thing being trained to become the model? If a model means "already trained," what is it before being trained? Is the model not the network that awaits training data? Or is the model just the weights applied to some standardized network?
The network before training is not very interesting, and so not many people talk about it. You can refer to it as "blank network", "untrained network", or any number of ways. Nobody refers to it as "a model".
Yes, if you want to, you can refer to the untrained network as "a model", or even as "a sandwich". But you will get confused answers as you are getting now.