The MAX7219 and MAX7221 are designed especially to drive 7 segment LED display units. While the 7 segment displays is the natural target they _can_ also be used to drive 8x8 LED matrix.
The difference between the MAX7219 and MAX7221 is that the latter is 100 % SPI compatible but the MAX7219 is not. The difference is the way the CS (Chip Select) pin is handled. In the MAX7221, data will only be "received" if the CS pin is low. This means the MOSI, MISO and CLK lines can be shared with other SPI devices. The MAX7219 will receive characters no matter the state of the CS line and the CS line is only used to latch the data. In short, the MAX7221 can share the SPI line while the MAX7219 need a dedicated one.