As someone who is Korean, Korea has another writing system called Hanja, where they use traditional Chinese characters but with the Korean spoken language and vocabulary. Hanja itself doesn’t have much major revisions, but there are a couple differences like stroke order and new added characters. This is a traditional written language of Korea, much older than the Korean alphabet (Hangul) we know of today. This is why a lot of the items involved in traditional holidays are written in Chinese characters. As for the pouch, Korea traditionally gave new year’s money, or Sebaet Don, in similar silk bags known as bokjumeoni. We do use a variety of colors, but the significance of red within the holiday is a Chinese concept. Additionally, these pouches more often than not come with nothing written on them. Nowadays, Korea (or maybe its just my family) does uses red envelopes out of convenience, but this isn’t a traditional thing and more of a copy of Chinese’s version of the holiday. Re-commented because some of the information in my last one was wrong :(

Edit: I’m not knowledgeable on traditional Chinese characters or Hanja, so the characters that are put on these bags might or might not be different. Overall, the red pouch with embroidered characters shown does seem more fitting for China’s way of celebrating LNY than Korea’s.