There are two forms of electrostatic air cleaners.
The classical electrostatic air cleaner has a fan which blows air between a series of charged plates. The plates are charged with a high voltage, Odd numbered plates are charged positive and the even plates are charged negative (or visa versa). A series of charged wires charges the dust and pollen particles as they enter the space between the plates (with the airflow). With use the plates are covered with the crud removed from the air. These air cleaners are made in various sizes ranging from table top to cabinet sized, to units which mount in the air return ducts on forced air systems.
The ionizer is a simplification of this. It eliminates the need for a fan and provides a source to charge duct (pollen etc) particles in the air near the unit. Ionizers rely on drafts and convection currents within the room since they can only charge particles near the unit. Charged particles are deposited on nearby surfaces.
Twenty years ago I had an ionizer. I left it on the top shelf of a bookshelf. When I moved after three years, I was startled to find the wall behind the unit was almost black. I had to pay the landlord to repaint the room. Since that time I have used a classical electrostatic cleaner.
The Sharper Image tower air cleaners appear to be hybrid technology.
The 'Deluxe Spire Feel-Good Fan with Negative-Ion Feature' is an ionizer with a fan. The 'Ionic Breeze' units appear to be a hybrid. They collect dust on blades, but don't have a fan. I am skeptical that without a fan they can move enough air between the paltes to be useful. The UV lamp seems like a gimmick.
I now have an electrostatic cleaner mounted on my furnace made by Honeywell. Trion used to be the leading maker of the tabletop of cabinet air cleaners. Some Trion cleaners were sold under the Sears name. I don't know if they still are sold by Sears.