The labels apply to people, to statements and to surprises. A hawkish surprise is any event that shifts the expected rate path higher than what was priced, and it sells off the front end regardless of who said it.
The trap is confusing direction with surprise. A cut delivered alongside a hawkish dot-plot and a statement that removes the easing bias is a hawkish cut, and bonds can fall on the day the Fed eases.
Example: the Fed cuts 25 basis points as fully priced but the median 2026 dot rises by 25 basis points. The 2-year yield rises 9 basis points on a day the policy rate was cut.
Related: dot-plot, fomc, rate-cut, terminal-rate, forward-guidance