One of the main differences is duration. An anaerobic event will be shorter than an aerobic one, usually lasting somewhere between a few seconds and two minutes, as anything longer than that begins to require aerobic function. The body simply cannot sustain an anaerobic effort for very long as the muscles are being flooded with lactic acid because of the intensity of the effort and the inability of the blood to cycle all of it out. Events such as a 100m dash or the pole vault are strictly anaerobic.
An aerobic event is one lasting longer than a minute where the body depends on aerobic capacity, the ability to process oxygen and keep the muscles clear of lactic acid up to a certain point. Something like the 10,000m or a marathon are very much aerobic events.