The cell shown in your PDF document is a Galvanic cell. It converts chemical to electrical energy by means of redox reactions and yes, electron transfer. The inert electrodes are named according to their environments and their nature themselves. The right (-) electrode is the
anode because iron has a greater
electrode potential (ability to oxidize). Analogously, the left (+) cathode is the
cathode. The electrode with a better oxidizing ability is the one in whose vicinity
oxidation occurs.
If we take A to be the anode and C the cathode, then:
: \mathrm{Br_2 (aq) + 2\,e^-}\rightarrow\mathrm{2\,Br^-(aq)})
.