When looking at reports from within Projector, you'll see the following references to time and cost cards.
This page explains the differences between the different types.
Time entered against a billable project. A billable project is one where you could charge time if you wanted to. A time card can be "billable," but the client was charged nothing for it.
Time entered against a billable project with positive billing adjusted revenue on it. Essentially indicating you plan to charge the client for it. A time card that has been written down to zero, is considered non-chargeable. This terminology is generally only useful for Time & Materials or Not to Exceed engagements. Fixed Price engagements generally consider all hours chargeable unless they are explicitly written down to zero. The short definition you can ask yourself for all three contract types is - Does the card have at least one penny of Billing Adjusted Revenue associated with it?
Time entered against a non-billable project. Time that has been written down to zero against a billable project is not considered non-billable.
Your installation has various time off reasons defined. Hours logged against this is considered time off. These hours are not classified under billable, non-billable, or chargeable. Time off does not include holiday hours like New Year's Day. That is tracked under a separate category called "Holiday."