Why I need SPI pins to be duplicated?

Setup: a sketch doing GET from google.com runs on Arduino UNO R3 +W5100.

I have W5100 connected to UNO as a mezzanine : W5100 is just placed on top of the arduino board.
Then I started to figure out what pins are really necessary. Simply it looks like I have stacked the boards using flexible wires instead hard stacking one board over another one. Then remove one wire between boards, connect arduino to USB check COM port output, repeat…
The wires really needed to do GET request are of course 5v power and GND and SPI pins.
What surprises me is that I need SPIs duplicated for some reason!!!
Why I need to connect both ICSP SPI pins together(W5100 ICSP to UNO ICSP) and pins 11, 12, 13 together(W5100 pin 11,12,13 to UNO pins 11,12,13 )??? Why just ICSP or Digital pins are not enough but I need both groups of pins?? Pin 10(SS) - this is the only that does not rise any question cause no duplication for this pin on both W5100 and UNO.

This is the Arduino Uno R3 schemetic.
The pins 11,12,13 are connected to the corresponding pins on ICSP. So you need to connect to one of those set.
And you need to connect pin 10(SS) with SPI CS pin on W5100.

This is the Arduino Ethernet shield schemetic. Please refer to this.
The SCK, MOSI, MISO on W5100 are connected to the corresponding pins on ICSP.
And the SPI CS pin on W5100 is connected to the pin 10.

If both pictures for UNO board could you, please, also show the SPI CS pin on W5100 ?

The SPI CS pin on W5100 is SCS.
Also i want to say you that SPI Enable pin (SEN) should be connected to 3.3V to use SPI.

If just pins 11,12,13 and 10 are used to connect UNO and W5100, the need for manual press of the RED Reset button of W5100 chip exists for my sketch to do GET.