DVI Difference?

The main difference with DVI is DVI-D and DVI-I. DVI-D carries a digital only signal, whereas DVI-I carries both a digital and an analog signal.

The DVI-I port and cable will have extra pins that are designed to carry the analog signal (google DVI-D and DVI-I images and you can see the differences) and are capable of being converted using a DVI-I to VGA adapter. The DVI-D, lacking the analog signal, cannot.

You'll just need a DVI-D cable to use with your adapter.

Edit: You can use a DVI-D cable with a DVI-I monitor without issues, but if your monitor is DVI-D and your cable is DVI-I the pins will interfere. That's why I suggested a DVI-D cable, and since you won't need the analog signal, that should be okay.