Arduino ethernet shield outputs behave differently than Uno's

I am trying to control a number of relays using Uno+Ethernet shield. I have this little test sketch that runs after connection to the router is established (I removed all the Ethernet connection stuff for clarity).

int rel[]={0,1,2,3,4,5,6,7,8,9,10,11,12};
int i;

void setup() {
  for (i=1;i<13;i++)
  {
    pinMode(rel[i], OUTPUT);
  }
}

void loop() {
for (i=1;i<13;i++)
  {
    digitalWrite(rel[i],HIGH);
    delay(1000);
    digitalWrite(rel[i],LOW);
    delay(1000);
  }
}

However when I connect my relay board to Ethernet shield's pins 1 to 12, four LEDs of the four corresponding relays are half lit although the relays switch on and off as instructed by the code above. What I also don't like is this trebling sound during relay switching on. If I detach the shield and connect the same relay board to the corresponding Uno's pins and load my sketch onto Uno rather than Arduino Ethernet board, none of the LEDs are :confused: lit (as expected) and I can hear a very clear relay switching sound.

I thought Ethernet board's digital pins are just replicated from the Uno but it looks like this is not the case. Or am I missing something? Would be grateful for any hints.

After a few hours of experimenting, it looks like Ethernet shield uses digital pins 1, 10,11 and 12 for something else. When I remove all the Ethernet instructions, the remaining sketch runs fine even with Ethernet shield attached. And one more lesson - you do not upload to Arduino Ethernet board, but to the Arduino Uno itself.

From the reference https://www.arduino.cc/en/Main/ArduinoEthernetShield

Arduino communicates with both the W5100 and SD card using the SPI bus (through the ICSP header). This is on digital pins 10, 11, 12, and 13 on the Uno and pins 50, 51, and 52 on the Mega. On both boards, pin 10 is used to select the W5100 and pin 4 for the SD card. These pins cannot be used for general I/O. On the Mega, the hardware SS pin, 53, is not used to select either the W5100 or the SD card, but it must be kept as an output or the SPI interface won't work.

How about pins 0 and 1? I understand pin 4 can be used for SD card only, not for controlling relays?