What is the definition of an "objective kill"?

Based on experience you get an Objective Kill when you kill (or damage) an enemy player while he is on or near the objective.

Meaning that on payload maps an enemy player would need to be actively pushing or contesting the payload.

Same goes for point captures, where, to get an objective kill, an enemy would need to be on the point that is to capture or to defend.

This also means that you cannot get more Objective Kills than normal Kills.