A language model in computer science is a model that predicts the probability of a sentence or a word given a sentence. This definition predates LLMs.

A 'language model' only has meaning in so far as it tells you this thing 'predicts natural language sequences'. It does not tell you how these sequences are being predicted or any anything about what's going on inside, so all the extra meaning OP is trying to place by calling them Language Models is well...misplaced. That's the point I was trying to make.