I am not exactly sure, but my gut feeling is that Cursor existed before Claude Code was released, and the term vibe coding existed already at that time.

EDIT: Okay, Andrej tweeted about Vibe Coding on February 3rd 2025, and Claude Code was released in the same month. But Cursor was already there (I can see usage starting January 2025 in my account and know that it took me a few weeks before I tried it).