"A private message, personal message, or direct message (abbreviated as PM or DM) is a private communication channel between users on any given platform. "
They are all private in terms of intended recipients. They're not cryptographically protected.
On and Off I try with Twitter, but it just doesn't work for me. I would delete my account, but there's so many companies and services who are only accessible via their Twitter accounts, that without an ability to message them, you can't raise an issue.
As an interesting (well, to me) side note, a few months ago I migrated away from being 'Jaruzel' on many sites to 'MattOwen_UK'. Within 24 hours of switching my account name on Twitter, someone else had grabbed @jaruzel. I was surprised at the speed that happened.
It's PM god damnit!