everything has a hull regen rate. Capitals just have base and then per level upgrade. I never saw ships in combat regenerate per second, but every 5 or so seconds.
Active Tank is actually more like the Vasari self-repair and what's used in eve by way of armor repair units.
Passive is just loads of hull points and armor.
Nano-Tank, for lack of a better term, is where you boost the regeneration rate not just 100%, but near 1000% or 10x the base regen + per level for capitals. Boosting regen rate 10x can give a L6 capital like the Vasari colony capital with a base regen of 1.5 and per level .1 a regen rate of 10 x 2; 20 hull per second. I've not seen per second regen in combat, but only every 5 seconds or so and regeneration (based on vanilla vasari colony cap) of about 50 (based on constants file: InCombatHullRegenerationPenalty 0.5).
I don't know if there is a hardcoded thing that calculates regen every X seconds or if the game just does that. I think we are 'stuck' with only increasing the hull regen percentage.