It recently occurred to me that while an ADC will build significant AD and moderate armour pen assassin types like 
will go ahead and build mostly armour pen items. After reading about how armour works I was wondering what the pros/cons are of each or if they are pretty much the same way to get to an end game.
The thing is assassins deal most of their damage with skills, those skills have base damage scaling without buiyng any AD. Penetration helps them to get that damage onto the champ.
ADC rely mostly on their auto attacks. They first need to build AD so that they have damage to penetrate with.
i love it when i build 2 armor pen items on zed and deal 389 damage per auto when i only have 319 - 328 ad
So ADCs and assassins take two completely different build routes. Assassins build attack damage and armor pen, with little regard to other stats in most cases. An ad assassin build might look like:
Just as an example. This provides a crap ton of armor pen, including a crap ton of flat armor pen, and then some attack damage and a drop of attack speed/crit. This is ideal for dealing more or less true damage to moderate armor targets- anything below ~150 armor or so. It works very very well for achieving high burst in combination with skills that deal physical damage and scale with AD, but doesn't do that much DPS. On the other hand, ADCs want to go for the multiplicative scaling of AD+Attack speed+Critical strike. In the hyper-old school build, this looks like:
Now, that's pretty outdated as an adc build path, but I think the differences in terms of what stats they give should be pretty clear. This second build gives %armor pen only, no flat. It gives very high crit chance compared to the other, some good attack damage, and high attack speed. That combines to make it relatively more effective against VERY tanky targets, and not necessarily so good versus squishy ones. This build provides far higher DPS, but doesn't necessarily provide the best burst.
ADCs build for DPS, so they build AS, AD, and Crit, all multipliers of each other that best facilitate DPS.
Assassins build for burst, this leads them to ignore AS, to be replaced by the next best multiplier; Armor pen.
It's a default build path caused by playstyle optimization, nothing more.
