By mistake, when using Notes, I started killing and yanking instead of cutting and pasting and it worked. Same seems to be true for Pages. What gives? I don't think I have ever tinkered with the standard settings (at least directly).
Those key bindings are programmed into the standard text handing routines by Apple. Unless the programmer goes out of their way to write a text input library on their own, you get those key bindings for free.
Same as the close/minimize buttons and much else that is similar between programs. Much of a program comes from Apple's frameworks and SDK.