Hypergen has superior regeneration, is not treated as an Aura for gem handling.
Overgen has inferior regeneration, IS treated as an Aura for gem handling.
In a nutshell, one is a guaranteed draw (with high enough gem handling) but has lower regeneration ~Overgen~ and one has a random chance to be drawn at some point during the fight regardless of your gem handling skills but has higher regeneration ~Hypergen~. That is the difference between the two gems.
Also, because Glitch knows his maths, here's a handy chart:
100% increase means you double something.
200% increase means you triple something.
300% increase means you quadruple something.
Generally, Nod math is multiplicative for similar effects that stack, except for vampiric effects, which add. That means that if you have regen from a pet (say 75%) and regen from a rune (say 50%) and regen from an aura (say 100%), you would multiply them together (1.75x1.50x2.00=5.25x or 425% regen).
As always, make sure you read ALL of the description, because things like Overgen/Hypergen act very differently as to how they are drawn based solely on the description.
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