You're not off-base at all. The way I think about it:

- LLM = the model itself (stateless, no tools, just text in/text out) - LLM + system prompt + conversation history = chatbot (what most people interact with via ChatGPT, Claude, etc.) - LLM + tools + memory + orchestration = agent (can take actions, persist state, use APIs)

When someone says "LLMs have no memory" they're correct about the raw model, but Claude Code or Cursor are agents - they have context, tool access, and can maintain state across interactions.

The industry seems to be settling on "agentic system" or just "agent" for that last category, and "chatbot" or "assistant" for the middle one. The confusion comes from product names (ChatGPT, Claude) blurring these boundaries - people say "LLM" when they mean the whole stack.