Having a Board doesn't mean you have two sets of governing officials. Your bylaws have to define who makes up the Board of Directors, and it's perfectly fine to say something like "The Officers of the organization constitute the Board of Directors." It's also fine, if you want to, to have the Board made up of the officers plus some other people, but that still doesn't give you two sets of governing officials.
You have one set of governing officials: the officers. Together, with or without other people, they constitute the Board.
The key distinction is where the power lies. Your officers should have specific powers and duties, and should not be empowered to act outside those specific powers; the Board -- not any individual officer, and not the officers individually, but the officers collectively -- should have the general governing power.
This might be clearer if we look at an example. Your PTO probably needs an annual budget. You might make it a duty of one of your officers, the Treasurer, to prepare such a budget for approval, but you should not give the Treasurer the authority to approve the budget. It's perfectly reasonable to give the authority to approve the budget to the officers collectively -- that is, the Board -- who will discuss it and vote on it. (Depending on your organization, you may want the entire membership to have the authority to approve a budget rather than just the board, but budget approval is a reasonable and common power for a Board to have.)
Other powers a Board commonly has include setting a meeting schedule, establishing and dissolving committees, setting policies, directing which bank(s) to deposit funds in, and so forth.
Hope that helps!
