From Berny

The following is an interesting post from Finescale.com forum from Berny (former USAF) on the subject of air to air missile smoke trails.

The early AIM-7's and AIM-9's left a large smoke trail behind them. After the rocket motor burned out the missile would go into a coast mode but still tracking the target. Depending on how far the target was from the shooter would depend on the coast mode. At twenty miles the last five miles would be coast mode for the AIM-7. At six miles the last mile would be the coast mode for the AIM-9. These heavy smoke missiles are no longer being used except for live fire until the rocket motors are used up.

Later versions of the AIM-7 and AIM-9's and the new AIM-120 use low smoke rocket motors and the range was improved. The rocket motors would fire longer thus giving the missile longer range. The actual range is still classified so I can't give you an example. They still left a smoke trail but not as heavy as the early versions.

Russian missiles leave a large smoke trail. They are just begining to build missiles with low smoke rocket motors.

When you see a live fire at a target aircraft (drone), the target is "making smoke" so it can be tracked by the camera aircraft. You can see the heavy smoke from the drone and missile as they impact. It is really something to see from the air.