Many products - including toothpaste and polishing compounds - contain abrasive materials that create friction and scouring action when rubbed against a surface.
Scouring powders or cleansers contain abrasives commonly used to clean and remove stubborn stains that are slow to respond to chemical action alone.
However, use of an abrasive cleaner may scratch and damage smooth finishes such as porcelain, fiberglass or enamel, making it even more difficult to clean the surface in the future.
New kitchen and bathroom fixtures do not require a scouring cleanser to clean them of soap films and body oils. Dissolving soil by soaking with the correct non-abrasive cleaner (especially a foaming type that sticks to the surface) then wiping and rinsing usually does the job.
When cleaning older, abused fixtures, choose the mildest abrasive cleaner available — such as a Soft Scrub®-type product or baking soda — and apply just enough that, with light pressure, the embedded soils are loosened and may be rinsed away.
A moistened pumice stone may be used to remove heavy mineral and rust deposits from porcelain toilet bowls.
Reference:
Don Aslett in The Cleaning Encyclopedia: Your A to Z Illustrated Guide to Cleaning Like the Pros.