Acuity means ‘sharpness of vision; the visual ability to resolve fine detail’. For example: “A person who is tired will have an impaired visual acuity.”
Another meaning of acuity, which is related to acute, is that it refers to “a quick and penetrating intelligence”. For example: “Gandhi was a man of great political acuity.”
Acumen, on the other hand, refers to ‘mental sharpness, intelligence, sagacity”. For example: “Einstein was a man with the greatest possible acumen”.
Last but not the least, acute carries a few different meanings. One of those is the one that is often referred o in geometry. It means ‘having a sharp point’: “Angles of less than 90 degrees are called acute angles.”
The 2nd meaning of acute is ‘extremely severe and sharp’; as an acute pain.
The 3rd meaning of acute is ‘keenly perceptive or discerning, ingenious’: “Einstein is said to have been a man of uncommonly acute intelligence.”
A usage for all of the above words: Samantha’ natural acumen in science suggested she had an acute sense of smell and a good visual acuity.