Where is the line between Anaerobic and Aerobic?
Anaerobic respiration is a respiration where the final electron acceptor is different than oxygen. The final acceptor can be a less oxidizing than oxygen, like sulfate (SO42-), nitrate (NO3-), or sulfur (S). For example bacteria that use sulfate are obligate anaerobs. 

The Krebs cycle cannot take place in the absence of oxygen, although oxygen is not directly involved in the cycle. The oxygen is required for the electron transport chain, which oxidized NADH and FADH2 back to NAD+ and FAD+, which are involved in the four reduction reactions of the cycle.

Thus, aerobic respiration includes both Krebs cycle and final electron acceptor of oxygen, whereas anaerobic respiration does not.