I had read that both perror() and printf() write to the terminal screen. But perror() writes to stderr while printf() writes to stdout. So, to print errors why is perror() used when printf() can do it.
printf() cannot write to stderr. fprintf() can. perror() always does.
There is no requirement that writing to either stdout or stderr writes to a terminal screen - that is up to the implementation (since not all systems even have a terminal). There is also no requirement that writing to stdout and stderr results in writing to the same device (e.g. one can be redirected to a file, while the other is redirected to a pipe).
perror() will be implemented with built-in knowledge of the meanings of error codes, represented by the static errno, which is used by various functions in the standard library to report error conditions. The meanings of particular values are implementation defined (i.e. they vary between compilers and libraries).