To send a message in Emacs, you start by typing a command (C-x m) to select and initialize the *mail* buffer. Then you edit the text and headers of the message in this buffer, and type another command (C-c C-s or C-c C-c) to send the message.
Begin composing a message to send (compose-mail).
Likewise, but display the message in another window (compose-mail-other-window).
Likewise, but make a new frame (compose-mail-other-frame).
In Mail mode, send the message (mail-send).
Send the message and bury the mail buffer (mail-send-and-exit).
The command C-x m (compose-mail) selects a buffer named *mail* and initializes it with the skeleton of an outgoing message. C-x 4 m (compose-mail-other-window) selects the *mail* buffer in a different window, leaving the previous current buffer visible. C-x 5 m (compose-mail-other-frame) creates a new frame to select the *mail* buffer.
Because the mail-composition buffer is an ordinary Emacs buffer, you can switch to other buffers while in the middle of composing mail, and switch back later (or never). If you use the C-x m command again when you have been composing another message but have not sent it, you are asked to confirm before the old message is erased. If you answer n, the *mail* buffer is left selected with its old contents, so you can finish the old message and send it. C-u C-x m is another way to do this. Sending the message marks the *mail* buffer "unmodified," which avoids the need for confirmation when C-x m is next used.
If you are composing a message in the *mail* buffer and want to send another message before finishing the first, rename the *mail* buffer using M-x rename-uniquely (Section 17.3). Then you can use C-x m or its variants described above to make a new *mail* buffer. Once you've done that, you can work with each mail buffer independently.