Kelly,
Is this the full language?
Typically, this type of language includes a requirement for Association approval to build or change anything on the exterior of the property.
Since the statement includes the word "or" I see this as a combination of two restrictions in one sentence:
No trailer, tent, garage, barn or other out-building shall be erected as either a temporary or permanent residence.
AND
(if one exists) No trailer, tent, garage, barn or other out-building shall be used as either a temporary or permanent residence.
I can also see how some might interpret it this way:
No trailer, tent, garage, barn or other out-building shall be erected.
AND
No trailer, tent, garage, barn or other out-building shall be used as either a temporary or permanent residence.
However, I suspect that you still need to get prior approval to have a storage shed.
Here is a link to a thread about interpreting statutes (works just as well with covenants):
http://www.hoatalk.com/Forum/tabid/55/view/topic/postid/103015/Default.aspx