OpenAI documents three separate crawlers, each controlled independently in robots.txt. Blocking one does not block the others, and they serve very different purposes — blocking GPTBot (training) has no effect on whether ChatGPT can cite you in search, which is OAI-SearchBot.
How to allow ChatGPT search but not training
A common goal is to appear in ChatGPT's search answers while keeping your content out of model training. Per OpenAI's documentation that means allowing OAI-SearchBot and ChatGPT-User while disallowing GPTBot:
User-agent: GPTBot → Disallow: / · User-agent: OAI-SearchBot → Allow: / · User-agent: ChatGPT-User → Allow: /
All three respect robots.txt per OpenAI's own documentation. Verify a request is genuinely from OpenAI against the published IP ranges rather than trusting the user-agent alone. Always confirm the current tokens on OpenAI's official page before relying on this.