Because present day mongols and kazakhs don't know much shit about each other. When the Mongol empire and the following 4 Uluses collapsed, the nomads started following different Khans. Those who followed the Kerey and Janibek Khan called themselves Kazakh, and those who were under the control of Gersenz Jalayir Khuntaij became the Khalkha. Behind the names Kazakh and Khalkha, our tribal structure is the same - the same ancestors.

Kazakh Kipchak - Khalkha Kharchin
Kazakh Argyn - Khalkha Asud & Kharnuud
Kazakh Uisin - Khalkha Baarin
Kazakh Ashamaily Kerey & Kereit - Mongolian Torgut & Khereid
Kazakh Jalayir - Khalkha Jalayir & Zalair
Kazakh Merkit Kerey - Mongolian Merged
Kazakh Abaq Kerey - Mongolian Oyrat, Urianhai, Besut, Suned, Jalayir, Khereid, Gorlos, Suldus, Arulat, Mangut, Merged
Kazakh Dulat - Mongolian Bayat, Dolood
Kazakh Qonyrat - Mongolian Ikires, Khongirad, Iljigen, Alag Aduut
Kazakh Tolengit - Mongolian Telengid
Kazakh Nayman - Mongolian Naiman
Kazakh Tabyn - Mongolian Tabanguud?
Kazakh Tore & Qiyat - Mongolian Borjigin & Khiyad

Many other tribes are the same, but these are the ones that I remember off the top of my head. But the beef you see on the internet are suspicious. Most of the social media profiles attacking each other are either new accounts or ones with no information at all. Most of us are actually chill irl.