Never mind. Just answered my own question. The first instance refers to a closed adiabatic system, and the second refers to an open steady-state adiabatic process.
I'm struggling to understand a concept which I assume is basic, but I can't seem to fit the pieces together. When speaking about an ideal gas, I understand that
ΔH = ΔU + Δ(PV) = ΔU + RΔT
So far so good. I also understand the relationship:
ΔU = Q + W... (W here is work being done on the...