Okay, let's start over. A Mac and Windows computer cannot read each others' drive as you've seen. You have several choices and depending on what you intend to do with the drive some are better than others. Before you make your decision think about why you want 1 drive for 2 computers and what you want to accomplish. Also read about Time Machine. Some choices will not work with Time Machine.
Your choices include:
1) buying a program to let your Windows computer read the drive as you have it formated now. The only downside is you'll spend about $35
2) format the hard drive so the Windows computer can read it and use a free program on your Macintosh so it can read and write to the drive. Don't choose this option if you want to use TimeMachine with the drive.
3) split the drive into two different sections (this is called partitioning) so that one can be formatted for Windows and the other for the Macintosh. The disadvantage is you have to decide how much of the drive to assign to each system and once the decision is made it is inconvenient (or worse) to change it.
4) reformat the hard drive using a system that both computers can read and write to. Like option 2, this keeps you from using the drive for TimeMachine
You don't have to understand all the ins and outs of the 4 options - we can guide you through the process once you've made your decision. Just think about how you want to use the drive and why you've chosen to use 1 drive between 2 computers. Come back and let us know your thoughts and we can guide you toward the best choice or at least help you eliminate some of the options.