It is better illustrated with animals. Birds have complex courtship rituals, this allows, usually the females, to select a mate. Once bonded they may stay together for life. However the courtship could be said to have been successful once consummation occurs.
I find the whole engagement and marriage thing artificial and ritualized. Males court females, ie attempt to gain their favor, in order to mate with them. This can be a long process or a short one. The idea is always the same, to raise her opinion of you so that she will accept you as a partner.
Before 1960, the typical life cycle included a long courtship and long-term marriage begun in the couple's early 20s.
Did "courtship" include "engagement" , or was it only the period before formal engagement?
"Courtship" officially ends when the couple gets formally engaged. There is a theory that the only reason some men get engaged (and then married) is so that they no longer have to "court" the woman. ("Court" in this case meaning to take her out on dates, to dinner, to the movies, and to buy her thoughtful little gifts on special occasions.)
(I probably didn't make the process sound nearly as romantic as thod00's description.... )