"Exhibition" or "exhibit"
Hmm, were those people you spoke to Americans?
In American English, Exhibit = Exhibition and they both mean the show of painting, photograph, or other artwork.
One obvious difference is that exhibit can also be used as a verb, but exhibition can't.
Although there are contexts where the two words are synonymous as nouns, I think most people would accept "exhibits shown at an exhibition", but not "exhibitions shown at an exhibit".
In short, an exhibit is far more likely to mean a single item being displayed, whereas an exhibition is more likely to be an event where many different things are displayed.
Having said that, this distinction is something of a Briticism. Americans don't use exhibition so often anyway, so for them exhibit tends to have both noun meanings, as well as being a verb.
AHDEL gives the following definitions of exhibit:
exhibit noun
The act or an instance of exhibiting.
Something exhibited: studied the dinosaur exhibits at the museum.
A public showing; an exhibition: spent the afternoon at the space exhibit.
Law Something, such as a document, formally introduced as evidence in court.
Judging from the third definition, exhibit and exhibition are synonyms, overlapping in OP's sense.