Air Ionizer, Air Purifier or Air Cleaner?

I'm a little confuse about this.

Air Ionizer, Air Purifier or Air Cleaner: What do they do?

I need one that I can put at home where it can clear germs. You see, sometimes my kids fall sick and their coughs can contaminate the air.

So, an air cleaner will be good.

If I search for a product that can clean the air, do I look for Ionizer, Purifier or Cleaner? Or something else?