What is the difference between rated current In and tripped current?

"Rated current" is the current the device (motor or transformer?) is designed to handle at full load. "Tripping current" is the current where a protective device (fuse, breaker) will open to protect the device from overload/overheating. "Tripped current", may be the current the tripping device measured prior to making the decision to trip, if you are reading this from a digital protective device like a relay or OCR.