The difference is that Esra is actually feminine, whereas Ezra very much isn't.
Well, actually,
Ezra seems to be a (rare-ish) Turkish girls' name*. And according to Turkish name sites, it seems to have a different etymology than
Esra or masculine
Ezra.
BTW, I'm not trying to contradict anyone or anything here, I just thought I'd use the opportunity to bring it up in the hope that someone more knowledgeable might chime in :)
* See:
http://tr.linkedin.com/pub/ezra-yakit/5a/425/519http://tr.linkedin.com/pub/ezra-yaz%C4%B1c%C4%B1/99/53a/687https://tr.linkedin.com/pub/ezra-kilinc/3/5a/303