Basically these are the techs which produce mods, which enable/disable cloacking abilities, you equip them, you can cloak,if you are UC you can cloak anyway and the techs just add cloaking level
Also US hero racials grant level 3 detection on T3 skill and pirates gain detection levels quite early.
Not-UC tree:



UC tree (as they start with cloak lvl 1 and imrpove afterwards) + they have a strong ambush mod on juggernaut tech:

It's ok if simplicity is not what you were looking for, let's revise what we know.
There are modules that provide cloacking and counter-cloacking abilities to FLEETS your SHIP with the MOD is in.
Those can be seen in the pictures above. As well as the fact that detection comes one tier later than cloaking, which institutes a sort of tech race.
You can NOT cloak juggernauts (no sneaki ion boom boom) nor obliterators (same reason).

To enable cloacking you need to have such module on your fleet.
Pro tip: You can also place said mods on a hero ship to provide effects.

To cloak press the cloacking button on the fleet:
Good we can cloak now! How does that help us?

Cloaking - UNDETECTED - means you can skip blockades, AMBUSH enemy fleets on engaging and also, they can't see you! ;)
You also can't siege, you have to DEcloak for that, DEcloacking means LOSING ALL MOVEMENT POINTS. Which is kinda ok if you are sieging anyway.

UNDETECTED means the opposing fleet does not have a detection level equal to your cloacking level or higher, or DETECTION PROBE of same ability deployed on system.

DETECTION PROBE is obtained by higher tiers of detection tech, they can be deployed and stay forever.
DETECTION PROBEs level up with the tech, so you can spam entire galaxy with cheaper level 2 detection, and then tech up to level 3 and BOOM!

AMBUSH is enabled wtih T3 cloacking mod and enables your FLEET to remain cloaked until they reach the RANGE dictated by the BATTLE TACTICS CARD you use.
This means that if you equip your fleet with railguns (melee heavy wep) and select turtle card, you usually win. Because you are invisible and can not be fired upon, until you are in melee range, at which rails rock! YEEEEY!
OFC ambush and any related bonuses (looking at UC ambush mod broken AF) are NEGATED when you are DETECTED.
To take best advantage of ambush mod, using melee weapons and tactics is encouraged.

Home system cloaking level = system level, min 1 (starts), max 3 (lvl 2 upgrade = the second one)
Sanctuary cloacking level = number of planets as sanctuaries, min 1 (start), max 3 (3 planets).
GZ now you get it ^_^

Detection of UC home works the same, you fly over it, see it, it's detected aaaaaand.. it's gone. Say hi to faction balancing.
You can NOT deploy detection probes on nodes, unless there is a detected UC home present, so it's a little tricky to find them after, best of luck!