API in this respect stands for Actual Packet Interval.
Basically it refers to the actual time that requested data will be delivered. In ControlNet because of it's scheduled data transmissions this can be calculated, but I am not sure that API figures can be calculated for EtherNet/IP for anything but best or worst case.
For ControlNet the API will be binary multiples of the Network Update Time (NUT). So given a 5ms NUT then the API values would be: 5, 10, 20, 40, 80ms. The API will be the closest lowest interval. So in the example I used if you ask for a 19ms RPI you would get 10ms. If you asked for 21ms you would get 20ms.
OG