What is the relationship between UART and printf within retarget?

HI.

I'm trying to understand the relationship between UART and printf within retarget.

as I understand, retarget supports to implement low level function fputc, if I want to use printf().

if I am right, I can't still understand the relationship between printf and UART_STDOUT.

especially, the below example is what I want to share you.

this is the hello.c example code.

//Hello.c

#ifdef CORTEX_M3
#include "CMSDK_CM3.h"
#else
#include "CMSDK_CM4.h"
#endif

#include <stdio.h>
#include "uart_stdout.h"

int main(void)
{ 
  // UART init
  UartStdOutInit();

  printf("Hello world\n");

  printf("** TEST PASSED **\n");

  // End simulation
  UartEndSimulation();

  return 0;
}

and retarget.c

#include <stdio.h>
#include <time.h>
#include <rt_misc.h>
#pragma import(__use_no_semihosting_swi)

extern unsigned char UartGetc(void);
extern unsigned char UartPutc(unsigned char my_ch);
struct __FILE { int handle; /* Add whatever you need here */ };
FILE __stdout;
FILE __stdin;


int fputc(int ch, FILE *f) {
  return (UartPutc(ch));
}

int fgetc(FILE *f) {
  return (UartPutc(UartGetc()));
}

int ferror(FILE *f) {
  /* Your implementation of ferror */
  return EOF;
}


void _ttywrch(int ch) {
  UartPutc (ch);
}


void _sys_exit(int return_code) {
label:  goto label;  /* endless loop */
}

I can't understand how does printf() work? Is printf() working as UART function as a fake ? or really works as UART?

Is printf() connected UART function? I can't understand the relationship between UART function of cortex-m3 and printf().

Does printf() differently work such as printf() of ANCI C?

Would you please anyone help me to understand this question to clarify?

Thanks in advance