Not sure what sort of definition you're looking for but:
Flameout: the flame in the combustion chamber is extinct, caused by a variety of factors e.g. Birds, stall, excessive water consumption
Roll back: the thrust is less than you've requested via the thrust lever but is still producing thrust. Anywhere between less than requested an idle.
Seized: rotational speed of a section of the engine has stopped entirely I.e. isn't windmilling in the airflow as you'd expect in a simple rundown. It signifies damage.
Failure: the engine isn't working. It doesn't differentiate between severe damage or a gentle run down that you may not even notice from the cabin.