Denture Cleaning Tablets for Coffee and Tea Cup Stains

True of harsh cleansers like Comet powder and Ajax and to a lesser extent Bon Ami. But not salt and baking soda.
These powdered cleansers are calcium carbonate based abrasive cleansers. They have just a little "scratch" to them. Please see "Mohs Scale" of scratch and "hardness" on Wikopedia. But they are rife with harch cleansers, bleach, and strong chemicals.

Calcium carbonate has a Mohs scale hardness of 3.5
For comparison, a fingernail has a hardness of 2.5. Glass has a hardness of 7, porcelain and glazing on ceramics and vitreous enamel on steel around 5-7.
You can scratch or polish your fingernail with calcium carbonate, but not glass. It's the acids, bases, and chemicals that are deteriorating the surfaces of tubs and cups over time. But, calcium carbonate can take off gold from grandma's fine china. Gold is a 2.5.
So, without all the harsh cleanser componants sodium chloride (table salt, a 2-2.5) and bicarbonate of soda (baking soda, a 2.5) are much more unlikely to scratch your glass ceramics, enamel, and china. Just don't leave either on the surface for long periods.