When should I use perror("...") and fprintf(stderr, "...")?

Calling perror will give you the interpreted value of errno, which is a thread-local error value written to by POSIX syscalls (i.e., every thread has it's own value for errno). For instance, if you made a call to open(), and there was an error generated (i.e., it returned -1), you could then call perror immediately afterwards to see what the actual error was. Keep in mind that if you call other syscalls in the meantime, then the value in errno will be written over, and calling perror won't be of any use in diagnosing your issue if an error was generated by an earlier syscall.

fprintf(stderr, ...) on the other-hand can be used to print your own custom error messages. By printing to stderr, you avoid your error reporting output being mixed with "normal" output that should be going to stdout.

Keep in mind that fprintf(stderr, "%s\n", strerror(errno)) is similar to perror(NULL) since a call to strerror(errno) will generate the printed string value for errno, and you can then combined that with any other custom error message via fprintf.

They do rather different things.

You use perror() to print a message to stderr that corresponds to errno. You use fprintf() to print anything to stderr, or any other stream. perror() is a very specialized printing function:

perror(str);

is equivalent to

if (str)
    fprintf(stderr, "%s: %s\n", str, strerror(errno));
else
    fprintf(stderr, "%s\n", strerror(errno));

perror(const char *s): prints the string you give it followed by a string that describes the current value of errno.

stderr: it's an output stream used to pipe your own error messages to (defaults to the terminal).

Relevant:

char *strerror(int errnum): give it an error number, and it'll return the associated error string.