A floor is a set of floorlets or interim period floors that are equivalent to put options on some reference rate. Floors are used to hedge against downside movements of the underlying.

On the other hand, a floortion is an option on a floor (which is, in turn, a bunch of floorlets). It gives the holder the right to buy a floor at a preset strike price for a specific premium at or by the expiration date of the floortion.

Both floors and floortions are options. However, the underlying in a floor is a rate, while it is a floor (on a rate) in a floortion.