GPTBot
GPTBot is OpenAI's web crawler used to collect training data; it is distinct from the agents that power search results shown inside ChatGPT.
OpenAI operates several agents with different purposes. GPTBot gathers training data. OAI-SearchBot supports search and the links shown in answers. ChatGPT-User fetches a page when a user follows a link.
Blocking GPTBot in robots.txt opts out of training use. It does not remove a site from ChatGPT's search results, because those use a different agent.
Why it matters
The confusion runs both ways: some sites block GPTBot expecting it to stop ChatGPT recommending competitors, and others allow everything while intending to opt out of training. Both are avoidable.