it depends on what you mean by differently.
in simplest of terms, think of the 595 as 8 switches that can be turned on and off by the computer ... it may also help to visualize each 595 as one "byte" in a buffer ... if you have eight 595's, you have an eight byte buffer. you can control each bit in each byte of that buffer, so the same holds true for a 595
in my
rainbow chaser project, I used three 595's connected in a daisychain to control 24 leds (eight rgb leds) ... I created different patterns by changing the bit sequence sent out to the string of 595s ... if there were leds that I didn't want changed, I just left their bits alone in the buffer
since the microcontroller pushes data out to the chips so quickly (20mhz / 8 = 2.5mhz serial clock estimated), the registers update so fast you can even do fancy things like time domain division... giving leds the appearance of different brightness levels (the waveform looks like pwm), but that is some fancy programming!
any microcontroller will work ... it depends on your application ... the inexpensive 16F628A or 16F88 are good all-purpose chips to start with ... the 12F683 and 12F639 are economical and very small pics, but are still very capable of running a large register of 595's.