According to her IMDB profile, she has a "writer" credit on "Jedi Crash" and "Nightsisters," and a "written by" credit on "Sphere of Influence" and "The Academy." If there's a distinction between the two phrases, I don't know the details.
My guess is the "writer" basically means she tossed around some ideas and somebody else wrote about them.
"Written By" implies she actually sat down at her computer, opened Final Draft, and started plugging away.
There's no such distinction. The writer of an episode gets a "Written by" credit for it -- they're just two ways of saying the same thing. If you just contribute ideas which are scripted by someone else, then the credit is "Story by."
IMDb is not entirely consistent or accurate; the distinction between "writer" and "written by" in its entries probably comes down to the vagaries of whichever contributor happened to post each entry in question. StarWars.com's episode guide, which is somewhat closer to the source, gives Ms. Lucas a "Written by" credit on all the cited episodes as well as "Monster," and I'm sure the screen credits were the same.
However, it's worth noting that The Clone Wars does include a credit of "series writer" on some episodes, which seems to be the equivalent of a story editor or the like, a staff writer who oversees or participates in the scripting process but doesn't do enough work on the actual script to get a "Written by" credit. But that's a distinct credit from writer/written by.
I thought Berman did nothing, except getting his picture taken from time to time...but he worked for Rick Berman
Oh, on the contrary, Berman was a very hands-on producer, directly involved in every major decision. That's well-documented in multiple behind-the-scenes books and articles.
But even if he had done nothing, that wouldn't invalidate my statement. Lots of people work for superiors who don't do any work themselves.