'Display' and 'exhibit'

The nouns exhibit and display are used in slightly different contexts.

Claudia asks an excellent question: 

Which of these two can be used is the sentence: "The director gave a detailed (display/exhibit) on the future plans for the art gallery."

Would you please explain to me the different meaning of these two nouns? 

A display in this context would be something that shows an example of something that can be generalized:

A display of strength.

The store's window display had a jacket I like.

Her trophies are in a display case.

An exhibit is used to refer to something specific, often in the context of a museum:

We saw the museum exhibit devoted to ancient Greek vases.

There's a new exhibit of contemporary art at the museum.

I was interested in seeing an exhibit of her work.

Note that idioms share this distinction:

On display simply means "being shown": 

The new televisions are on display in the store.

Exhibit A means "a perfect example": 

I use myself as exhibit A of laziness.

Finally, I wouldn't use either display or exhibit in this case. Here's what I would suggest:

The director gave a detailed presentation on the future plans for the art gallery.