As I was reading about Gaussian random variable (RV) and Chernoff Bounds, I came across sub-Gaussian & sub-exponential RVs. After much analysis, I still couldn't figure what purpose sub-Gaussian & sub-exponential serve in the broader realm of statistics.
So my question is: How do sub-Gaussian & sub-exponential RVs relate to Gaussian RV in an intuitive sense? How should I decide when sub-Gaussian/sub-exponential RVs are suitable for a particular scenario?
An answer combining intuition and mathematics would be helpful.