Fallacy of Exclusion Vs Hasty Generalization

The difference between these two is minimal and maybe only of real use in rare cases or to serious logic-nerds, but here goes:

In the Fallacy of Exclusion you fail to look at how the given quality is common among many groups, not just to the one.

In the Hasty Generalization you assume that the quality is common to all/most members of the given group (and you aren't really concerned with other groups).

Fallacy of Exclusion: I studied one and made a generalization about all ten.
Hasty Generalization: I only studied one group and failed to look for the same pattern in other groups.

Fallacy of Exclusion Example: "You shouldn't join a frat because they drink like fish."
Explanation:  But so do people in dorms. So do students who live independently off campus. So do most 18-20 year olds, including those who aren't students.

Hasty Generalization Example: "I met a student in a fraternity who's a racist.  I can't believe how racist fraternities are!"
Explanation:  I based an opinion about one million people on my experience with one or two.