Electronic — electrifies pollutants in the air to make them easier to trap.
Electrostatic purifier — charges particles drawn into the device with positive electricity. These particles are then attracted to the negatively charged aluminum collectors inside the device. This device can only remove the particles that pass through it, making it difficult to purify a whole room.
Electret air purifier — a special filter, which is called the Electret, is charged with electricity and when particles enter the filter they cling to that filter. The drawbacks are the same as listed for the electrostatic purifier.
Negative-ionizing purifier — This type of purifier produces negative ions in various ways (one way is through electricity run through metal needles — called "needlepoint") and releases them throughout the room. Thus a negative ionizer can reach farther distances than cleaners that just pull air through them. The way this works is that these negatively-charged ions changes the polarity of airborne particles so that they are attracted together. They then become too heavy to remain in the air and fall to the ground.
This type of cleaner does not trap the particles, only makes it so that they can no longer be breathed in. You can collect in some other way, such as vacuuming or dusting. Another downside of these cleaners is that they can stain the surfaces closest to them with the negative ions.