Any twitter management software is available like Outlook and thunderbird..
Since you asked about Twitter, I assume you know what Twitter is about, and am sure you have your own reasons for pursuing a Twitter management app with an interface akin to an email client.
That said, Twitter is fundamentally different from emails, and as such, "Twitter management software", or what is more commonly known as "Twitter clients" looks and operates very differently.
So far, I have not encountered a Twitter client that behaves even close to how Outlook and Thunderbird behaves. What I can recommend is what seems to be the favored Twitter client of Net users - TweetDeck.
Also, you might want to check out this two links to see if any other good Twitter clients suits your needs.
IMO; TweetDeck is probably the closest to the interface you are looking for (that I have come across).