Templates are not tied to a mailing list or a specific mailing. They are available to all mailings.
Please note: It is possible to display and amend the contents of a template directly from the detailed view of a mailing. By using copy&paste, you may select a copy of an existing template, use this to create a new template and then make any amendments required. This saves a lot of time and a lot of typing effort. For details see chapter "Show template data".