This guide is detailed but short, wiki is confusing af so here is a summary of what I learned and a dummy down version to help better understand.
Agents
First lets go over agents.
There are four tiers of agents indicated by their lightning effects around them. In terms of strength here is what it looks like
Green Blue Static (Classified as Rookie) < Bold Blue Static (Classified Junior) < Purple Static (Classified Senior) < Gold Static (Classified Super)
They symbolize similar but different tiers of strength when fighting or in help capturing.
Fugitives
There are also 4 tiers of strength but in this case, pay attention to the color of the name. In this case vs agent, Light Blue Static is the same as a Green name.
The Tier goes Green < Blue < Purple < Orange
The Capturing
Green Fugitives can be caught by anyone except for a slight chance of the rookie.
Blue Fugitives can be Caught by Junior/Senior/Super
Purple Fugitives can be caught by Senior/Super
Orange Fugitives can be caught by Super
Mailbox Responses
You have two responses to two replies you can do, we will refer each response as A or B.
Here is what they look like paired up and what they do:
A - None of your business! --> A - So you're trying to trick me? | A + A
You fight the Agent and get W-Tads, a soul, and a relic named after a permit.
A - None of your business! --> B - Sorry sir, I really have no clue! | A + B
It ends the encounter. Period.
B - What do you want? Tell me more. --> A - Oh, I happen to know something... | B + A
There are two ways this can go, it can be captured depends on the rankings shown above or escape.
If it is captured you only be getting b-tads.
If it escapes you will have a chance of them coming back and seeking revenge for greater rewards.
B - What do you want? Tell me more. --> B - Sorry, I know nothing about that | B + B
This has a rare chance to lead to the Fugitive giving a reward as a thank-you.
You can actually tell the difference if B+B has a two minute wait on it instead of it saying the mail ends here.