The word toothbrush came from the two parts of the word, first a countable noun and then a verb or noun. The action of brushing teeth with a toothbrush is basically the use of the invention of Joseph Addis. Addis worked on the toothbrush while he was in jail. First, he saved a bone from one of his meals and poked some holes in it. The prison guard gave him some bristles. He tied the bristles into little bundles, cut them to make them even, put glue on the ends, and stuffed them into the holes.
The original form of tooth cleaning and gum massage was by using a chew-stick.
When Joseph Addis invented the toothbrush, it was meant for tooth cleaning.
Here are some examples of Nouns that are derived from Noun (countable) + Noun/Verb combination with the same structure:
Snake pit (also snakepit) - a pit filled with snakes.
Fish tank - there can be two or three kinds of fishes in a fish tank and not just one fish. Many fish in a fish tank.
Matchbox - A small cardboard box in which matches are kept.