'\0' evaluates false, "\0" evaluates true

Inspired by a program described in K&R section 5.5:

void strcpy(char *s, char *t){    while(*s++ = *t++);}

C program

if ('\0') { printf("\'\\0\' -> true \n"); }else      { printf("\'\\0\' -> false\n"); }if ("\0") { printf("\"\\0\" -> true \n"); }else      { printf("\"\\0\" -> false\n"); }

prints

'\0' -> false"\0" -> true

Why do '\0' and "\0" evaluate differently in C?

clang version 3.8.0