At the file descriptor level, stdin is defined to be file descriptor 0, stdout is defined to be file descriptor 1; and stderr is defined to be file descriptor 2. See this.
Even if your program -or the shell- changes (e.g. redirect with dup2(2)) what is file descriptor 0, it always stays stdin (since by definition STDIN_FILENO is 0).
So of course stdin could be a pipe or a socket or a file (not a terminal). You could test with isatty(3) if it is a tty, and/or use fstat(2) to get status information on it.
Syscalls like open(2) or pipe(2) or socket(2) may give e.g. STDIN_FILENO (i.e. 0) if that file descriptor is free (e.g. because it has been close(2)-d before). But when that occurs, it is still stdin by definition.
Of course, in stdio(3), the FILE stream stdin is a bit more complex. Your program could fclose(3), freopen(3), fdopen(3) …
Probably the kernel sets stdin, stdout, and stderr file descriptors to the console when magically starting /sbin/init as the first process.