Both air purifiers and ionizers do the same thing: clean the air. Where the two differ, however, is how exactly they achieve this goal. Air purifiers clean the air through a mechanical process, while air ionizers use electricity to trap harmful particles in the air.
There are several methods that air purifiers use to scrub the air. For the majority of in-home appliances, these include Ultraviolet Germicidal Irradiation (UVGI), filter-based cleaners and activated carbon filters.
The majority of air filters are designed to run for long periods at a time, so they've been engineered to run quietly. Some of them have other features, such as programmable operation so that you can have them run at certain times and various cleaning modes.
Because air filters use a filter to trap materials in the air, occasionally the filters need to be changed. UVGI filters operate a little differently. What they do is circulate air in front of a series of ultraviolet lamps, which sterilizes the air as it passes through.
Air Ionizers operate somewhat differently than air filters. What they do is run the air through a field of ions, which are generated by an electric field. The ions in this field attach to dust particles in the air, causing them to be attracted to a charged collector plate in the ionizer. Some concern has been raised by the EPA and other consumer bodies, because these purifiers produce ozone as they operate.
There is also some debate over the effectiveness of air ionizers. Several organizations have claimed that air ionizers do more harm than good because of their production of ozone. However, there is some scientific evidence to back up the claim that air ionizers might help in combating Seasonal Affective Disorder.