It gets extremely blurry, because people commonly refer to any model that uses a component associated with the Transformer architecture as a Transformer (i.e. using some kind of QKV-esque attention mechanism). I think it's easier to think of it like this:

A large language model is just what it says--a very large statistical model trained for language tasks. This covers the spectrum of GPT-style models, but also those hard to classify ones, like Liquid's "Liquid Foundation Models", which can get up to 24 billion parameters and use grouped query attention, but are closely related to state-space models as well: https://huggingface.co/LiquidAI/LFM2-24B-A2B

Also, as others have pointed out, a Transformer isn't inherently a language model. So really they're sort of two different axes, one classifying the model size and task, the other referring to a specific architecture.