In practice, SqWebMail is somewhat tolerant of the mailbox contents being changed in a middle of a session by another mail client, accessing the same account. Still, all bets are off, and be aware of potential consequences (such as clicking on one message, and the message coming up blank, or another message appearing).
What really happens is that when you delete a message, SqWebMail will create a hard link into the Trash folder, then mark the message as deleted in the original folder. When you leave the folder, SqWebMail will go through the folder and unlink all deleted messages.
Moving a message to another folder works exactly the same, except that the message is linked into that folder, instead of Trash.
If you move a message to another folder, and you immediately go back to
the folder contents window (or you move a message directly from the folder
contents window), the message will show up as deleted. If you try to move
a message again into another folder, this operation will quietly fail
without giving you an error message.