The social media app Xiaohongshu (小红书) does literally translate to "little red book" in English. However, this is completely different from Mao's famous work, which was never called this in Chinese. Mao's book was informally known as "Hongbaoshu" (红宝书) meaning "red treasured book" and formally titled "Quotations from Chairman Mao Zedong" (毛主席语录).
The apparent connection in English comes from translators using "Little Red Book" for both terms (maybe due to training or an agenda? who knows, choosing word-by-word translation for one and popular translation for another), even though they're distinct and unrelated in the original Chinese, and of course in the official desired English "RedNote" too.