Yes, that's right. Logically, based on word origin and derivation, "crescent" should mean "growing," but it doesn't. The word "crescent" mostly refers to a shape--the narrow curved shape of a crescent moon. The waning moon has the same shape, so it is "a crescent." A popular item at breakfast is a "croissant," which we pronounce "craw-SAHN." It is a delicious roll that is baked in the shape of a crescent. It is sometimes even called "a crescent roll" instead "a croissant." "Croissant" is the French word for "crescent," borrowed into English--and used only for rolls. In ordinary life in the US, most people are not very aware of the moon's phases. We recognize full moons. Only people interested in nature notice the "old moon in the new moon's arms,." The word "gibbous" is found only in articles about astronomy. I have been astonished to find that many people have never noticed that you can often see the moon during the daytime! Within the last few years, the press has gone insane telling us about colorful names for different kinds of full moon--harvest moon, wolf moon, pink moon, supermoon, "blue moon," etc. Some are old traditional names that are being revived.

Yes, we don't distinguish. A crescent moon refers to either the waning or waxing moon.