‘Passive’ means the module is always giving it’s bonuses, cannot be turned off or on and doesn’t use capacitor.
‘Active’ means you turn it to get the bonuses, either at the right time or just all the time while in combat if your capacitor allows.
While both shield extenders and shield amplifiers are passive they’re very different modules.
A better comparison for shield amplifiers is shield hardeners; both module types give your ship shield resistances. Amplifiers do so automatically/passively, while hardeners have the downside that they use capacitor (and cannot be used when your capacitor is empty). Hardeners also have some upsides:
- they give you more resistances than amplifiers
- like many other active modules they can be overheated for even stronger bonuses
- they come in a ‘multispectrum’ variant that gives you resistances to all types instead of just one
So how do shield resistances compare to shield hitpoints from a shield extender?
Resistances reduce the damage you take. Say you have 50% thermal resistances and you get hit by a thermal missile: you only take half damage.
A shield extender won’t reduce damage, instead it increases how many shield hitpoints your ship has.
A better comparison for the shield extender is the shield booster. Both of these modules add hitpoints to your ship, while the extender does so passively and the shield booster does it actively: a shield booster repairs some missing shield hitpoints any time you activate it.
Shields in EVE will automatically repair over time, which is ‘passive shield regeneration’. Shield extenders will improve how much you repair, but likely not as much as shield boosters.
These two modules each have their up and downsides:
Shield Extenders:
- passive, so they need no capacitor
- increases your total hitpoints (your 'shield buffer’) so you can survive short high bursts of damage well
- increases passive shield regeneration
- increases your ship’s size, which is a downside as it allows enemy ships to hit you more easily
Shield boosters:
- requires a lot of capacitor each cycle
- no increased shield buffer, you can get one-shot
- heals more than extenders
- doesn’t make you easier to hit like extenders
Sometimes one is better than the other, depends on the circumstances.
Hopefully some of the differences are clear.
Now your question: you want to know if you should train shield amplifiers for your PI alts?
I would skip it.
My own ships for PI are fit with shield extenders and multispectrum shield hardeners as shield modules. Extenders because you want some buffer, multispectrum hardeners because they give resistances to everything and also more than amplifiers.
Amplifiers can sometimes be worth it, but usually hardeners are better.