What is the American word for 'tea-towel'?

I guess they are called:

Dish towels:

• a rectangular piece of absorbent cloth (or paper) for drying or wiping

  • A tea towel or drying-up cloth (English), or dish towel (American) is a cloth which is used to dry dishes, cutlery, etc., after they have been washed.

  • In 18th century England, a tea towel was a special linen drying cloth used by the mistress of the house to dry her precious and expensive china tea things. Servants were considered too ham-fisted to be trusted with such a delicate job, although housemaids were charged with hand-hemming the woven linen when their main duties were completed.Tea towels have been mass-produced since the Industrial Revolution.

Ngram - BrE: dish towel/tea towel/drying-up cloth/dishcloth.

Ngram - AmE: dish towel/tea towel/drying-up cloth/dishcloth

(from Wikipedia): Towel.

I am American and familiar with "tea towel", but I think more commonly you'll see them called "kitchen towels". I would be surprised to find them in a gift store - they don't strike me as very collectible items. That may be the larger cultural disconnect.

As an American, I can tell you that we have many different absorbent materials in our kitchens. Here's an inventory of ours, along with the typical uses.

• Dish towel - always kept clean of food or hand contamination, used only to dry clean dishes after washing them. Sometimes known as flour-sack towels, they are flat, 100% cotton. They are often printed with a design, or occasionally embroidered for decoration. These are what you would likely call tea towels.
• Kitchen towel - multipurpose towel used for hand drying, counter drying, and absorbing food or drink spills in an emergency. Generally thicker than a dish towel, often made of a terry cloth. These tend to be more utilitarian, and generally not as decorative as a dish towel.
• Paper towel - disposable paper towels used for many of the same purposes, but also for cleaning up non-food messes (dog accidents, mud, heavy grease, etc) where there is no desire to contaminate a food prep towel.
• Dish rag - A small towel used for scrubbing dirty dishes.
• Sponge - Almost all kitchen sponges are artificial, made of open-cell foam. Larger ones are used to absorb large quantities of spilled liquids, smaller ones are used to hold a soapy mixture for scrubbing dirty dishes. Some sponges may have a non-abrasive plastic mesh on one side for aggressively scrubbing baked-on foods from pots and pans.
• Scrubbing pad - often called by a brand name, such as a Brillo pad or a Scotchbrite pad, these are a stainless steel mesh and are used to aggressively scrub baked-on foods from pots and pans.

Mirroring John Deters' answer, here is an inventory for the British kitchen (well, Home Counties English - I'm sure there are further local variants):

• Tea-towel, or drying-up cloth - [=JD's Dish towel] clean, thin, absorbant, passed from generation to generation until disintegrating. Commemorative pictures, flowery patterns, rude phrases.
• Hand towel - towel for drying hands, when in the kitchen. Made of terry cloth, fluffy, plain.
• Kitchen towel, or paper towel, or kitchen paper - paper towel, on a roll. Only with patterns if you have some sort of obsession or spend too much time in the supermarket.
• Dishcloth, or J-cloth - a cloth, generally damp, used for wiping dishes during washing. And for occasional worktop spills. Required to be blue or green and white gingham pattern by laws of decency.
• Sponge - yes. Usually with scouring pad on the top.
• Scourer - green, scratchy flat cloth, used to remove stubborn things from metal pans. Capable of destroying the nice china, non-stick surfaces. Sometimes a brillo pad or other metallic pad instead, or as well if enthusiastic.
• Bridget brush - plastic-fronded brush with a long handle, for attacking pans, jugs, glasses that are hard to clean with the sponge/scourer; often non-stick friendly. Best ones are pink.
• Bottle brush - wire-bound brush with radial fronds and a long handle, for poking inside bottles where nothing else fits. White, and for those over 45 only.