It is a pretty practical distinction.
So, since apparently I may need to clarify my actual point: For most people, an LLM-plus-agent-harness is just "LLM" or "AI". If you're trying to build one, you care about the distinction. Ditto if you're a pedant. But most people are not either of those things.
Go to a huggingface repo, look at the files, they have a literal chat_template.jinja