Twitter is a social service that's constantly growing and changing, rolling out small and not so small updates on a regular basis.
Their changes may not be quite so sweeping (or as controversial) as Facebook but the site is always evolving, and they've added something pretty crucial in a recent update. It's now possible to share a Tweet with someone else via a Direct Message.
It's a very useful feature, taking a topic out of the public sphere rather than just @-ing another user, and can be accessed very easily. Just long press on the tweet and you'll get a popup with the option to share via Direct Message. And if you're not on the app, you'll find the option under the 'more' button.
So get DM-ing!