The answer to that do you need them both question is actually "It Depends". Let's step back a second. External DVD drives may require more power than a single USB port provides.
On top of that although USB ports are supposed to provide a standard amount of power. On some computers they don't supply enough power to provide power to your DVD drive. The manufacturers have created these dual head USB cables that hook up to two USB ports so they get double the amount of power.
On those weird cables you'll see a full straight through cable that provides data and power for the USB drive and there is a little nubby one hanging off of that to plug in and get extra power. I would try it without the little nubby one and if it works you don't need the extra power.
On the other hand if it doesn't you can then plug in the second head on the USB cable and get enough power for your external drive. If one side of the cable works you can replace that funny cable with a standard USB cable so you don't have to keep track of an extra dangling bit hanging off the cable.