what is the difference between == and -eq in an if statement?

Question

Having the following for simplicity:

while
    echo -n "Does the command include flag(s)? (Y/N): "
    read option
    echo "option: '${option}'"

    # Is mandatory use `==` and NOT `-eq`
    if [[ $option -eq "y" || $option -eq "n" || $option -eq "Y" || $option -eq "N" ]]; then
      echo "Valid option"
      break;
    else
      echo "Invalid option"
    fi
  do :; done

If an input of a number is applied it works how is expected: Invalid option appears, but when any character is used how input always Valid option appears and it is not correct, but if is used (observe now == is used and not -eq)

while
    echo -n "Does the command include flag(s)? (Y/N): "
    read option
    echo "option: '${option}'"

    # Is mandatory use `==` and NOT `-eq`
    if [[ $option == "y" || $option == "n" || $option == "Y" || $option == "N" ]]; then
      echo "Valid option"
      break;
    else
      echo "Invalid option"
    fi
  do :; done

All work how is expected from the beginning.

So what is the difference between == and -eq in an if statement?