The short answer is no -- no one can define these terms. Since everyone uses the terms before defining them, they mean many things in different contexts.
I don't want to contradict Coach K., so perhaps I will just expand on what I think "old" definitions are, based on the contexts I have seen, in case you stumble across information written before common acceptance.
These are all terms to describe some physiological phenomena, although they are often associated with a specific effort or a workout.
Aerobic Threshold is the one I least understand. I find it useful to think of the Aerobic Threshold as the boundary between Endurance and Tempo runs, and as the boundary between "fat-burning" and "carb-burning". I'm sure both interpretations are factually wrong, since Endurance and Tempo Runs are both aerobic, and it probably has nothing to do with identifying the fat/carb burning boundary, but it doesn't matter, because the term is not used that much, and is basically the least important.
Anaerobic Threshold is associated with the point where lactate accumulation (triggered by the production of energy anaerobically) is no longer controlled, and generally signals the beginning of the end of your exercise. The effort is often estimated as your 1 hour race pace.
Using the terms "aerobic" and "anaerobic" to describe the thresholds are problematic, as faster efforts like 10K and 5K races are still mostly aerobic, hence the respective thresholds aren't really aerobic/anaerobic in nature.
Lactate Threshold is usually equated to Anaerobic Threshold, and is a better term in that it avoids the aerobic/anaerobic confusion. I say usually, because I have seen Lactate Threshold equated to Aerobic Threshold, while another term "Maximum Lactate Steady State" was equated to Anaerobic Threshold. Lactate Threshold is also often equated to Maximum Lactate Steady State.
Tempo runs are used to improve your Lactate Threshold, either as continuous steady state runs (up to 1 hour?), or broken up into long (10-20 minutes) repeats.
Sometimes the two thresholds are defined in terms of measured blood lactate, e.g. 2mmol and 4mmol, but these measures can vary from athlete to athlete, and changes with improved fitness.
VO2max corresponds to the maximum volume of oxygen you can consume during exercise, in ml/kg/min. Your 3K pace seems like a reasonable estimate for the effort. Some claim that a VO2max plateau has never been shown, and therefore a maximum doesn't exist. I believe it is not infinite, so it should be possible to find a reasonable upper bound, or accept the results of a VO2max test, and not debate about the existence of a plateau.
Improving your VO2max is usually achieved by short repeats (typically 3K to 8K pace) with short recovery, often called VO2max Intervals, or Aerobic Capacity Intervals.
Anaerobic Capacity Intervals are also short repeats (e.g. 1600m pace), but with longer recoveries. These kind of repeats are not associated with your terms.
Some links with useful descriptions of threshold definitions and discussions:
http://www.mcmillanrunning.com/training1.htm
(see sidebar)
http://www.lactate.com/threshold.html
http://home.hia.no/~stephens/lacthres.htm
http://home.hia.no/~stephens/vo2max.htm