SPI master and slave operating frequency
You have three different frequencies here. The master has a clock frequency of 4MHz. The slave has a clock frequency of 16MHz. The SPI interface has a transfer clock determined by the SCLK line. This is generated by the master, and can be any frequency you choose as long as a) the master can make it and use it b) the slave can accept it and c) it's fast enough for your transfer speed requirements.

Usually SPI masters and peripherals have dedicated hardware shift registers, that handle the high speed requirements of the clock, and only demand or present whole bytes to the controller.