What is the difference between a non-profit corporation called an
"Association" and one called a "Trust"?

It may be a formal incorporated not-for-profit corporation that does
not have shareholders, though it may have members and issue membership
certificates or require member loans. It may also be a trust or
association of members. The organization may be controlled by its
members who elect the Board of Directors or Board of Trustees.
Not-for-profit organizations may have a delegate structure to allow
for the representation of groups or corporations as members. It may be
a non-membership organization and the board of directors may elect its
own successors.

Association
A voluntary association (also sometimes called an association) is a
group of individuals who voluntarily enter into an agreement, explicit
or implicit, to form or act as a body (or organization) to accomplish
a purpose.

Trust
A trust is a legal arrangement for the control of property on someone's behalf. 

http://en.wikipedia.org/wiki/Non-profit_organization