Blackboard has two separate messaging systems: (1) an internal messaging system called "Messages", and (2) an external messaging system called "Email".
If you use Tools > Messages or Course Tools > Messages, then the messages you send stay within Blackboard. You can send and receive Messages, and the students can check their messages and reply within Blackboard using Tools > Messages. You will find folders in Messages similar to the ones you would see in an email client (Inbox, Sent).
If you use Tools > Send Email or Course Tools > Send Email function in Blackboard, then the email will go out of Blackboard and into the Internet email system (to the students' email). Email is external to Blackboard, so when students reply, their replies will go to your email inbox (Outlook, Northeastern webmail, Lotus Notes, Gmail, Yahoo, Hotmail, etc.). Email replies will not be sent back into Blackboard. Email delivery via the Internet may not be instantaneous. In the event of delay, the Internet will try to re-send messages for several days until it is delivered.
We hope this clarifies the Blackboard messaging system. Thanks for using Blackboard!