Yes, in fact it has an entirely different system prompt from the ones that Anthropic publish on https://platform.claude.com/docs/en/release-notes/system-pro...

The Claude Code one isn't published anywhere but it's very easy to get hold of. One way to do that is to run Claude Code through a logging proxy - I was using a project called claude-trace for this last year but I'm not sure if it still works, I've not tried it in a while: https://simonwillison.net/2025/Jun/2/claude-trace/