It sounds redundant to me; I don't believe that exact and precise have significant differences as is the case with many common phrases in english ("cease and desist", "each and every", "aid and abet", "always and forever", "hopes and aspirations", "last will and testament", "null and void", "over and above " etc).
NOW this being said, in scientific terms there is a difference:
Usually, accuracy, precision, and exactness are related to how reliable a measurement is. The measurement can be anything from weight to color.
Accuracy is a measure of how close to the actual value a measurement is. For example, a scale that measures 98g, 103g, 97g, and 102g when the actual weight is 100g could arguably be considered accurate, since it is decently close to the actual weight of 100 grams.
Precision is a measure of how close each measurement is to each other. For example, if a different scale measures weights of 106.5g, 107g, 106.7g, and 106.3g when the actual weight is again 100g, then it is very precise but not as accurate.
Exactness is the quality of an instrument or a measurement having good or perfect precision and accuracy.