Strange behavior performing library functions on STDOUT and STDIN's file descriptors

Throughout my years as a C programmer, I've always been confused about the standard stream file descriptors. Some places, like Wikipedia^[1], say:

In the C programming language, the standard input, output, and error streams are attached to the existing Unix file descriptors 0, 1 and 2 respectively.

This is backed up by unistd.h:

/* Standard file descriptors.  */
#define STDIN_FILENO    0       /* Standard input.  */
#define STDOUT_FILENO   1       /* Standard output.  */
#define STDERR_FILENO   2       /* Standard error output.  */

However, this code (on any system):

write(0, "Hello, World!\n", 14);

Will print Hello, World! (and a newline) to STDOUT. This is odd because STDOUT's file descriptor is supposed to be 1. write-ing to file descriptor 1 also prints to STDOUT.

Performing an ioctl on file descriptor 0 changes standard input^[2], and on file descriptor 1 changes standard output. However, performing termios functions on either 0 or 1 changes standard input^[3][4].

I'm very confused about the behavior of file descriptors 1 and 0. Does anyone know why:

• writeing to 1 or 0 writes to standard output?
• Performing ioctl on 1 modifies standard output and on 0 modifies standard input, but performing tcsetattr/tcgetattr on either 1 or 0 works for standard input?