Why does the Sun have different day lengths, but not the gas giants? The Sun's rotation period varies from about 25 days at the equator to about 38 days at the poles. As I understand it, this is because the Sun is not solid, and because of the way centripetal force works, the equator must move faster than the poles.

Question: if this works, why do Jupiter/Saturn/Uranus/Neptune have well-defined days? Why don't the equators of these planets rotate faster than the poles as well? For example, Wikipedia's article on Jupiter gives the length of a Jovian day as 9h 55m 30s, which is so precise that it implies Jupiter does not have a rotational period which varies with latitude.
It's a matter of how "day" is defined.

Wikipedia's article on Jupiter cites this IAU/IAG paper for the length of a Jupiter day.  In it, footnote (e) of table I has the following:


  The equations for W for Jupiter, Saturn, Uranus and Neptune refer to the rotation of their magnetic fields (System III)


The radio emissions of the gas giants have well-defined periodic variations.  These variations are caused by the rotation of the magnetic fields of those planets, and are evidence that they have a reasonably coherent core of some sort that's rotating at a uniform speed.  The periodic variations then represent the rotation speed of that object, which is taken as the rotation speed of the planet.

We're reasonably certain the Sun doesn't have a coherent core.  Measuring the variation of the magnetic field doesn't show a well-defined period, and doesn't provide a useful definition of the Sun's rotation speed.