The word exposure has been in use since the beginning of photography. To take a picture, you expose photosensitive material to a controlled amount of light. This material could be a chemical emulsion spread on a film or a glass plate, but nowadays, most probably, it is a digital chip like the CMOS sensor that is the heart of your Nikon D-SLR. The word exposure is used in more than one sense as shown in Fashion Retouching Los Angeles.
An exhibition is almost synonymous with a photo, the first photographers would have talked about doing an exhibition, while the most recent 35mm film allowed 24 or 36 exposures. Now the word is used more frequently to indicate the important choice of the right amount of light to get to the sensor. One of the most important and indisputable things about photography is that the light level changes.