Mechanical cause, which is sometimes called efficient cause or historical cause, is the description of an event, an object being moved, in terms of pressures and magnitudes of physical motions and forces acting on the event. Final cause is a description of an event, an actor acting, in terms of the end, purpose, intention, or that for the sake of which the event is done. A mechanical cause looks to the past, and asking what bumped into what to make the event; a final cause looks to the future, and asks what the actor feared or desired or anticipated.
In a recent discussion in this space, the question arose concerning final cause versus mechanical cause, and two objections were raised. The first, if I understood it, was that final cause, properly so called, did not exist because all final causes could be reduced to a recitation of mechanical causes. The other was that final causes are prescientific.