As verbs the difference between engage and impact
is that
engage is while
impact is to compress; to compact; to press or pack together.
As a noun impact is
the striking of one body against another; collision.
As verbs the difference between engage and conduct
is that
engage is while
conduct is (archaic|transitive) to lead, or guide; to escort.
As a noun conduct is
the act or method of controlling or directing.