The standard Arduino library is written for the W5100 Ethernet controller (W5200 and W5500 support are soon to be added). Your shield uses the ENC28j60 Ethernet controller, which is not supported by the Ethernet library. That's why you need to use the UIPEthernet library, which was specifically written for ENC28j60.
This is something you'll need to pay attention to with many libraries. They are written for specific hardware. If you try to use them with hardware they weren't written for then of course they don't work.