The question was: What are such "heavy tailed" distributions are called?

Answer and explanation: The correct answer is leptokurtic. "Kurtosis" the amount of data in the tails of a distribution. A leptokutic ditribution has more data in the tails (like the outliers shown in each of the 4 groups) than a normal distribtions does.

These links give more information on the topics mentioned in the question:
Kurtosis (leptokurtic and platykutic)
Homoscedasticity (the opposite of heteroscedasticity)
Skew

Boxplot of time by condition