The new look Twitter allows you to run more than one twitter account, which is useful if you have a business Twitter account and a personal account or if you are running accounts for more than one client.
The image is from an Android tablet, but to use this function is the same whether it is for apple iphone, blackberry smart phones or any android powered phones or tablets

To add an extra account go to me> Switch account >Add account Input the Twitter username and password
You can now switch between accounts and send and receive for your chosen account