No, they use significantly higher voltages to actually have small pollutants precipitate. Ionizers tend to not go that far.
That doesn’t seem to follow from the Wikipedia article on them, which seems to say one is the same as the other. Though there’s a third option with a similar name that is used without a filter https://en.wikipedia.org/wiki/Electrostatic_precipitator
How does it not follow? The Wikipedia article even lists ionizers as a separate article.
Ionizers are described as "air filtration using electrostatic attraction", while the ESP page I linked as the alternative specifically lists being filterless as its distinguishing feature, and is described as typically using lower voltage in home applications.