Yeah but "little red book" (xiaohongshu) in mandarin is not actually how the original Mao Little Red Book is called in Mandarin, either formally or informally. Informally in mandarin it's called hongbaoshu (literally "red cover book" and formally, as you can imagine, is like Quotes from Chairman Mao).

So this is a case of translators with an agenda translating two phrases with different original mandarin renditions (hongbaoshu and xiaohongshu), and picking and choosing the style of translation (base on usage vs based on character) to get the English translation to merge both of them as "Little Red Book".