Material conservation is the conservation of a quantity moving along with the flow. For adiabatic motion potential vorticity is materially conserved.
Local conservation is the conservation of flux of a quantitity through a fixed box.
Relative vorticity and mass are locally conserved. An active tracer is transported by the flow and affects its course. Potential vorticity is an active tracer since velocity depends on streamfunction which can be diagnosed from potential vorticity by PV-inversion. A passive tracer is transported by the flow without affecting its course. Chemicals can be considered as passive tracers.