Let us start with the pecking order and the signals sent out
when these terms are used - the code if you speak.

Manager is used when the job is primarily concerned with the business
and financial management of the museum.
Director has a slight upmarket connotation and tends to be used
when the message is one of administration, recommending policy to the
Board, slightly more freedom in running the place
Curator, now here is the rub. Curators have been traditionally
concerned with collections but since many in the museum profession
are not even aware of what "the material culture" means in terms
of curatorship we are left with a word that has many meanings and
none.
Director/Curator in an ideal world means someone with a knowledge of
the material culture with administrative ability to run a musuem.
Sometimes it just means someone who works for a museum where many
tasks must be done by a few.
Maurice D. Smith, Director/Curator, Marine Museum of the Great Lakes.