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.