I'm still waiting for my morning coffee to percolate... but I'll have a crack at this without caffeine..forgive me for any in-eloquence
1) When a compartment reaches an NDL limit, is it correct to describe that compartment as saturated or is that term reserved for true saturation dive with the compartment truly is saturated at equilibrium?
In recreational (no-deco) diving, the 'controlling' compartment will be the tissue compartment that reaches NDL first. On a single dive, that will be the fastest compartment. On repetitive and/or multi-day dives, it may be a slower compartment - because the slower compartments will be the ones retaining nitrogen from previous dives (slower half-times to off-gas).
The NDL limit doesn't necessarily correspond to complete saturation. That depends on which tissue compartment is controlling. The compartment half-time versus ascent speed plays a critical role in this. NDL in recreational diving is the state where the diver retains the ability to ascend directly to the surface at a given controlled speed. Thus, the NDL indicates a level of saturation that can be safely off-gassed within the parameters of that direct, controlled ascent. For fast tissues, that
may permit complete tissue saturation. For slower tissues, it won't.
In essence, staying inside an NDL means you are limiting tissue saturation to a level where it can be off-gassed sufficiently (within 'M-Values') on a direct ascent to the surface. The controlling tissue compartment half-time must be sufficiently fast to permit controlled ascent (usually ~10mpm) to the surface (1atm) without absorbed nitrogen reaching a critical pressure where it will leave tissue solution and form bubbles.
For simplicity, recreational diving assumes a constant maximum ascent rate. Tissue saturation and safe off-gassing has to fit within
that parameter. This restricts dive depth/duration to the faster tissues.
When you exceed an NDL, a slower compartment (or compartment
s) are sufficiently saturated to become controlling. The longer-deeper the dive, the more slow compartments are saturated. Ascent speed equates to the time needed to sufficiently off-gas those compartments. Deco stops are merely a means to limit that descent speed, whilst simultaneously maximizing the time spent with the greatest safe pressure differential across the lungs-blood-tissue (using nitrox deco gas
also maximizes that differential).
True saturation - as I believe the term is used in commercial diving - indicates
all theoretical tissue compartments are fully saturated (at or beyond six half-times) to ambient pressure, even the slowest ones.
2) Are "fast" compartments fast because they on gas faster or because they can hold relatively less? (I.e. is the compartment "faster" or "smaller"?)
In deco calculation (the math) tissue 'speed' is dictated entirely by the half-time. That half-time speed is a constant for a given compartment. As others have said, it is only a mathematical construct. The primary factor believed to dictate tissue on/off-gas speed is vascular supply - how much blood supply reaches a given tissue. Bones have little, fat a little more, muscles lots.. Given that body mass isn't a factor used to calculate deco, we can assume that current theory doesn't place much emphasis on the volume of gas held by a given tissue compartment.
In Deco for Divers, Mark describes half-time speed (via vascular supply) in an analogy - that of a warehouse loading trucks for delivery. The limitation on delivery is caused by the number/frequency of trucks that arrive to be filled up - rather than the size of the warehouse.