Twinkle vs. Twitter usernames: when and where?

I'm trying to find a pattern in how Twinkle uses tapulous/twitter usernames. Lets see if I have this right:

--> in the 'Nearby', the display is the tapulous name. When you reply, it replies to the tapulous name (? -- unsure)
--> In the 'home' display, there is both? The question I have is under *my* posts, it's under either my twitter name, or my tapulous name. Why either?
--> In the 'messages' display, I don't know. Ps -- anyway to delete private messages?

I'm just trying to figure out when and where Twinkle uses the twitter id of a twinkle user, or the tapulous ID of the twinkle user. Can a dev shed some light on this?