What is the relationship between MySQL pages and operating system pages?

By MySQL pages I mean this:


and operating system pages:


I understand both of them, but I do not understand their relationship. So the DBMS is basically a program that works over our correct O.S? So, why do not DBMS like MySQL use only the size of the operating system page, but let the DBA decide how big the page is?

what happens when the size of the O.S page is 8 KB while the DBMS is 16 KB? and if his vice versa?