The language of the yetis is actually very limited: they rely heavily on sounds and body language more than words, such as snorting, growling, roaring and also rely heavily on the tone of their speech when speaking to convey meaning. They don’t have individual words for everything = for example, they have no word for Pitch or Bogeyman, instead, the general phrase is (in my headcanon language) “Oorni bak” (trying to keep in line with the way they sound in the movie - lots of rolling “r’s” to sound like growling and sharp “ck” or “k” sounds for when they click their -very sharp - teeth together) which means “bad man” and would be accompanied by an angry snort to represent the sound the horses/ nightmares make.
However, that same phrase “Oorni bak” can also mean “bad” as in “naughty” and “man” as in “boy” – so when speaking of Jack Frost, they would use the same phrase, but this time accompanied by an exasperated sigh. While the phrase is the same, they would also say it completely differently for both characters – for Pitch it would be said more forcefully, snarling the “r” sound more with a sharper click on the “k” while for Jack it would said more like a grumble or a sigh, emphasising the “oor” sound.
Body language is also important, as mentioned. Keeping with the example “Oorni bak”, accompanying the harsher, stronger way they say it for Pitch and the angry snort to represent the nightmares, they would also square their shoulders and narrow their eyes, and perhaps try to make themselves look even bigger if they felt threatened.
On the other hand, when talking about Jack, the exasperated sigh and grumbling tone would be accompanied by a shake of the fur to represent being cold, eye-rolling and sagging shoulders as if they were getting tired of his antics or (if he was present and being a little shit) crossed arms, an unimpressed glare or maybe even an angry shake of the fist to convey their annoyance towards him.
This is just one example of many, but hopefully covers the main areas of what I believe the Yeti language is like. In summary:
Limited number of words in their language
Sounds, body language and tone are very important
Same words/ phrases have different meaning depending on how they’re said.
Bonus: Yetis also have their own set of insults, some of which can’t be translated to English, or don’t have an English equivalent.
Extra Bonus: The worst Yeti insult imaginable is “Itkadagu Gak-tu!” The aftermath of saying this to a Yeti will always result in a fight, and a bloody one at that.
North is a lot like a father figure to Jack. North was probably a ladies’ man when he was young. Combine 1 & 2, and I think North will sometimes try to teach Jack how to flirt, since Jack is getting more believers by the day. And he has Jack practice on Phil. Phil is not amused. (But goes with it anyways because North tells him to.)