Aerobic respiration is on a cellular level. It's how cells produce energy, aerobic: Energy production in the presence of oxygen, anaerobic: Energy production without the presence of oxygen.
Your question whether aerobic respiration is the same as respiration took me back to my school days! I thought I would just add a little more to addicted's great answer. No, aerobic respiration isn't the same as respiration: The opposite of aerobic is anaerobic respiration.
Respiration is the process by which energy is released from glucose. Glucose is stored the liver, but created in the pancreas.
Aerobic respiration needs oxygen. When glucose reacts with oxygen, it creates pyruvic acid which creates ATP. Here are the word and symbol equations:
glucose + oxygen → carbon dioxide + water (+ energy)
C6H12O6 + 6O2 → 6CO2 + 6H2O (+ energy)
Anaerobic respiration doesn't use oxygen, because this is what happens when there is not enough oxygen for aerobic respiration to happen. This is the word equation:
glucose → lactic acid (+ energy)
Anaerobic respiration is for short, explosive activities such as the start of a sprint or the shotput action.
I found a good picture that shows you the difference between aerobic respiration and anaerobic respiration:
So that should explain your question about whether aerobic respiration is the same as respiration! Try having a look at this video from CrashCourse to show the differences between aerobic and anaerobic respiration: