DPhiE and DPhiE - same letters, entirely different organizations

[CutiePie2000]

I bet that Cream, shadokat and Siobhan will be first to respond here!

There are 2 Delta Phi Epsilon fraternities out there!
I was wondering about Delta Phi Epsilon (the NPC organization that Cream, shadokat and Siobhan are members of) and then there's Delta Phi Epsilon, the Professional Foreign Service Fraternity.

Part 1:
Since both GLOs have identical letters, I was wondering what is the relationship between the two DPhiE's?
Do they peacefully co-exist, sharing the same letters or is there any feeling of "Hey, you copied us?" It looks like the foreign service one is at about 23 chapters.

Part 2:
Are they are any other orgs that have 100% IDENTICAL LETTERS?
The only thing I can think of is:
Kappa Alpha Order and Kappa Alpha Society, but even then--one is an Order, one is a Society.

Anyone else got other examples of duped letters, identical names?