Win 10 64, nvidia 1060 6gb
Short description of error
Not render engine related. If you use the Defocus node in the compositor, and an animated object as the target for your camera to determine the focus distance, when you press ctrl+f12, the defocus won't animate, stuck at one distance, the one on the frame you had on the viewport before you pressed ctrl+f12. It seems the camera distance based position of the target object is not being evaluated when the animation is being composited. Animating the Distance value of the Camera directly, without an object, works though. And native eevee or cycles depth of field works with animated distance object too. This is not a huge priority or anything.
Exact steps for others to reproduce the error
Play the animation in the viewport and you'll see the distance of the camera focus does change, but render the animation with ctrl+f12 and the defocus doesn't change in the final video. Using eevee's internal depth of field or animating the distance value of the camera directly does work, and you can render that to compare.