The -min lines are for min delay analysis (for hold check), and -max lines for max delay (setup check). Usually we are using the worst corner library (SS process, high temp, low voltage) for setup check, and the best corner library (FF process, low temp, high voltage) for he hold check. This is why you have possibility to specify different diving cell (actually different library for the same cell). The -rise and -fall are for more accurate analysis, you may use them in conjunction with -input_transition_rise and -input_transition_fall (as an example).