Hold one picture: a length of cotton with oil pressed into it, so the surface turns smooth and the rain slides off instead of in. Every other meaning is that cloth wearing a different shape — cut it into a coat and the coat takes the cloth's name; add the trousers and the set takes it too. The grammar follows the picture: no article for the material, an for the coat, -s for the whole outfit.
From the word’s history
The source records the word as a compound of oil + skin: cloth given an oiled outer layer that keeps water out the way an animal's skin does. That reading matches the modern core, where the material sense comes first and the clothing senses are named after it.
資料把這個字記成 oil（油）加 skin（皮）的合體：布被抹上油，就多了一層像動物皮一樣擋水的外皮。這條線索正好對上今天的用法——材料的意思排第一，衣服的意思都是跟著布的名字來的。
Wiktionary, "oilskin"
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