An email message attachment is a file sent with an outgoing email message. Standard activities and functions allow outgoing email messages to include attachments. See How to send email with attachments.
A case attachment identifies a named small file, screen shot image, correspondence, URL or text note that a user or an activity has associated with a work item.
On the standard harness Perform and Review forms, the Attachment area and the provides access to add, edit, delete, or review work item attachments. Correspondence attachments are permanent parts of the history of the work item and cannot be deleted or updated.
A rule attachment is a file associated with a rule, saved as a separate (binary file rule).