"Clothes" has this definition in The American Heritage Dictionary of the English Language*:
1. Articles of dress; wearing apparel; garments. 2. Bedclothes
"Clothing" has this definition:
1. Clothes considered as a group; wearing apparel. 2. A covering.
From these definitions (excluding "bedclothes), one gets the idea that the individual garments comprise the category of "clothes," while the more abstract idea is found in the word "clothing."
There is a thread of logic here,since "clothes" is a count noun, and "clothing" is a noncount noun. There are other similar words that show the more concrete item as a count noun but the abstraction as a noncount noun: machine/ machinery; scene/ scenery; dollar/ money, etc.
("Clothes" comes from the word "cloth," but "clothes" is always a noncount plural noun. It takes a plural verb and plural modifiers: clothes are, many clothes, these clothes, etc.)
Similarly, the Collins COBUILD** gives this definition for "clothes: "Clothes are the things that people wear, such as shirts, coats, trousers and dresses...Moira walked upstairs to change her clothes....He dressed quickly in casual clothes."
This dictionary gives this definition for "clothing": "Clothing is the things that people wear. Some locals offered food and clothing to the refugees....What is your favourite item of clothing?...Wear protective clothing...the clothing industry."
You might think of "clothes" as the more everyday word, in sentences like these:
You'll have time to change your clothes.
We're going to the mall to buy clothes.
That store sells maternity clothes. That one sells baby clothes.
I need to clean out the clothes in my closet.
Think of "clothing" when you think of the more abstract idea of clothes:
They manufacture clothing.
Wear protective clothing when you enter that area.
People need food, clothing, and shelter.
* The American Heritage® Dictionary of the English Language, Fourth Edition . Houghton Mifflin Company. 2003.
**The Collins COBUILD English Dictionary. Harper Collins. 1995