You can have the desired result both for terminal and pipes if you remember to remove the control characters as well. This is hardcoded for two lines.
#include <stdio.h>
int
main ()
{
fputs("output1\n",stdout);
fputs("output2\n",stdout);
fputs("\033[A\033[2K\033[A\033[2K",stdout);
rewind(stdout);
ftruncate(1,0); /* you probably want this as well */
fputs("output3\n",stdout);
fputs("output4\n",stdout);
return 0;
}