takedown is the term used for situations where either a kill or an assist is acceptable, such as to trigger a passive effect. Some effects have a limit time in which kills or assists will qualify.

What counts as a takedown?

In martial arts and combat sports, a takedown is a technique that involves off-balancing an opponent and bringing him or her to the ground with the attacker landing on top. The process of quickly advancing on an opponent and attempting a takedown is known as shooting for a takedown, or simply shooting.

Do assists count as kills in league?

Wiki Targeted (Games)

An assist is the action of helping an allied champion kill an enemy champion. Assists can be scored by hitting the enemy within the last 10 seconds before their death. This timer may refresh after contributing subsequently to the kill.