Kanji Question: Udon or Wonton?

I saw this packaging in the store the other day and I got confused. The kanji on it says 饂飩, which was new to me, so I took a picture and sent it to a Japanese friend who told me that it is the kanji for udon.

Then a Chinese friend told me that the same kanji is actually one of the ways to write wonton in Chinese, with the other set of kanji being 雲呑 also for wonton. However, in Japanese, wonton is almost always written in katakana.

So at some point in history, when Japanese people invented udon, they used the kanji of wonton, so they used to equate them to wonton but gave it a different pronuncation...? If anyone knows what happened, let me know!