So, I was watching these vids on YouTube....

1. Is Erde Kaiser Retsu Erde Kaiser Fury?

2. What are these different versions?
There's this "Strike Version"
http://www.youtube.com/watch?v=-lwlTRet6Bs

Then a "Slash Version"
http://www.youtube.com/watch?v=ehxG6q6fwRE

1. I think so.

2. In Episode 2, in the Erde Kaiser sidequest, you make him of different parts, which makes up whether he has Strike, Slash, Pierce, or Thunder effects depending on which parts you use.

If I recall certain GS Campaign missions determine which parts you get for Erde Kaiser in Episode II. According to the faqs, the Slash type Erde Kaiser should be the most useful one.