No, but the area between the two thresholds (the 'aerobic training zone') is where you would normally train within to cause an improvement in (aerobic) fitness. (Jeskas reply was excellent! but I know that it helps to have a few different explanations of something like this topic, so I hope I can help a bit.. sorry if I put it too simply..)
A THRESHOLD is a point which when you cross it, you are leaving one thing and entering a new one (e.g a doorway is a threshold).
-The AEROBIC threshold is the point at which when you cross it, you are able to make aerobic fitness improvements. If you train under this, which is VERY lightly, you are not pushing yourself and staying at a level that is completely comfortable, which means none of the adaptations will occur that improve your fitness (fitness improvements occur when you work above the level of exercise your body is accustomed to -- after this exercise is completed, your body adapts so it will be better prepared for next time, which is really becoming 'fitter')
-right at the top of the aerobic training zone is the ANAEROBIC threshold, which when you pass above it you are entering the anaerobic training zone (i.e. your body is producing energy without oxygen, causing lactic acid levels to rise). You only usually exercise within the anaerobic training zone for very short bursts, or the negative effects will begin to outweigh the positives (esp. lactic acid build up). Athletes sometimes work above this threshold to improve their tolerance to lactic acid.
-These thresholds are measured by HEART RATE, i.e. there is not just a set time at which everyone passes a threshold/enters a training zone -- it depends on their heart rate, how fit they are. A trained athlete will have higher thresholds (i.e. it will take them higher intensity exercise to reach the aerobic training zone than an untrained person, because an untrained person will not required a very intense form of exercise in order to 'push themselves')
So basically there are 2 thresholds, aerobic and anaerobic,(think of each of the thresholds as a line, the aerobic below the anaerobic) and the, what you could call 'shaded area' in between these 2 lines is the area in which you would exercise within for any improvements in fitness to occur.
When I did this topic my teacher gave us a number of different resources about it as different points of view help (the same with any topic in PD - if u don't get something, read a few diff. textbooks for diff. ideas, sometimes one of these will make it more understandable). I know i'm stating the obvious, but hopefully some of this has helped someone.. =)