Explanation about True positives, False Positives and False Negatives

[Aichiimv]

Hi, I was wandering what are is the difference between "np.sum(detected_pts)" (true positives count) and "np.sum(detected_gt)" which is used to estimate false negatives count?. My understanding is that gt are the real points and pts are the detected ones ( within the radius), but what would be the difference if the r is big enough and why are not the same?. For instance, in a mall set, you have 5 persons and the program correctly identifies 3 of them. True positives will be 3, false positives 2 and false negatives will also be 2 and therefore that sums(detected) will be equal. I also get that both will be higher with a bigger radius but the gt one will be bigger that the pts one (Sometimes). Question is because in your paper you wrote as False Negative definition : "A false negative is counted if a true location does have any estimated location at a distance at most r" which for me is the same as True Positive definition wich is the same just from the point of the estimated location. And if it is a misspelling why False negative is not the same as False positive?
Thankyou for your attention