Cover and aim penalty for an overwatch shot triggered from enemy action

When using an ability that allows overwatch to trigger on enemy actions, not just movement, what is the penalty?

The overwatch aim penalty gets applied to all overwatch shots*. This includes normal overwatches and covering fire.
The explanation for this is that it is a reaction shot; a quick reaction by the soldier who fires his gun; therefore his aim is reduced as opposed to an "aimed" shot (normal shut during your turn). The aim penalty is therefore tied to the soldier taking the shot and is independent of what the soldier is shooting at (other aim buffs/debuffs can still have a stacking effect, of course).

But when an enemy takes a shot as opposed to running away; they will still have their cover because they never moved away from it.
Even if an enemy is behind full cover and side steps before taking a shot; the full cover will still be in effect. The side step itself is not considered movement and will not trigger an overwatch, but the shot (that caused the side step) will still trigger Covering Fire.

This does mean that Covering Fire reaction shots have a worse chance to hit than a normal overwatch shot. For this reason, you should only give CF to your soldiers with above average aim (and who have other reaction shot bonuses); or else you'll just be wasting bullets most of the time.

*Technically, it gets applied to all reaction shots. This includes overwatch shots, reaction shots that occur when a suppressed enemy makes a move, the Return Fire pistol shots, and other "automatic reaction shots" (e.g. the Close Quarters Combat perk in XCOM EW. It exists in XCOM2 too but I'm not sure if it has the same name).