Aerobic: USING oxygen, activities such as running long distance.
Anaerobic: ABSENCE of oxygen, running short term such as sprints.
Yes, there is a such thing called Over training !! For anaerobic people, they experience sympathetic over training symptoms (Sympathetic=speeds up bodily functions, increasing energy needs). Those who are aerobic kinds of people, they are susceptible to parasympathetic overtraining (Parasympathetic= slows down bodily functions, conserving energy).
With this said, anaerobic training is much more effective. You will burn calories much faster and speed up your metabolism. When doing you cardio, do a 3 minute walk and 1 minute sprint, then repeat for a total of 20-26 minutes.
Age is a major factor when speaking of Periodization and over training. As you can assume, younger clients recover more quickly than older clients. Over a lifetime of training, the body will decrease in recovery ability, but during that lifetime it allows for harder and more frequent training (As long as it becomes a ritual habit and not a once a month thing).