On and Kun have nothing to do with formality. On readings are chinese readings of the kanji adapted to the japanese sound system. They were imported together with the kanji over the course of history, so there's also different types (kan-on, go-on, tou-on), but that distinction is not really important to know. Kun readings are the spellings for the traditional japanese native words that then became associated with the imported kanji. So in short: on = originally chinese, kun = originally japanese. Not every kanji has both, although most do. And I'd not recommend learning all the readings of a given kanji in general.
The "kun" you're thinking of is this one.
https://jisho.org/word/%E5%90%9B-1
The one listed in kanji entries is this one.
https://jisho.org/word/%E8%A8%93
Coincidentally, in both cases, くん is the "on" reading (on'yomi) for both of those kanji.
Understanding what "Kun" and "On" mean
Hi, I'm probably asking something really easy but underneath each Kanji it says "Kun" or "On". Im thinking that the Kun is the honorific that you use for someone the same age or younger than you, but was is On? And please correct me if what I think about Kun is wrong.