FP = system (or person) flags this as true when it is not

TP = ... flags as true and it is

FN = ... flags as false but it is true

TN = ... flags as false and it is false

To turn these into rates, you normalize them.

e.g. TPR = TP/P = TP/(TP + FN) = 1 - FNR

etc.

These are characteristics of a classification system

You will also hear sensitivity (TPR) vs. specificity (TNR) often, particularly in medical contexts. In other contexts you'll hear Type I (FP) vs. Type II (FN) error.

In most cases you a set of trade offs in your algorithm, and will need to pick a balance between sensitivity and specificity.

c.f. ROC: https://en.wikipedia.org/wiki/Receiver_operating_characteris...