What is the difference between staged and unstaged fuel manifolds?
Staged means that fuel is delivered "after launch" instead of immediately.  This terminology is more familiar from staged rockets:


  At engine idle conditions, the electronic engine control (EEC) unit sends a signal to the BSV which then shuts off fuel flow to the ten staged fuel nozzles. As a result, the ten unstaged nozzles receive a higher fuel volume resulting in a stronger flame. [More fuel for those ten and none for the others, encouraging combustion: fewer flames, but bigger ones.]  As the engine accelerates above idle, the EEC signal commands the BSV open, allowing fuel to flow to all nozzles [more than the first ten] so the engine can operate at higher power settings.


This is quite like a campfire started with tinder (unstaged, ignites instantly) and then sustained with thicker wood (staged).

"Pilot fuel flow" is hard to google in an aeronautics context for obvious reasons, but it means the same as "pilot flame" for a household furnace or water heater.  It acts like a continuous low fuel consumption spark,
at start-up and low part load, to encourage more vigorous combustion shortly before that is commanded.