Not always!
While it is true that your ceiling fan is an active load heavier than most light fixtures, often you can screw the ceiling fan support bracket directly into the structural wood just outside of the existing electrical box.
However, if the structural wood does not sit in line with your electrical box, then you do indeed need to replace your standard ceiling box with a code-required “fan-rated” box, since the mounting screws are thicker for handling the weight and vibration that a ceiling fan needs.