A floorlet is a put option on some reference rate. It is an interim period floor in a multiple period floor. Hence, a set of floorlets make up a floor.

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