Today's post is a quick side note before we take up heirs' courtesy titles and how to address dukes: the difference between an heir apparent and an heir presumptive.
An heir apparent is an heir who will definitely inherit a title as long as he doesn't predecease its current holder--which, in the British system we're focusing on, means the oldest legitimate son of the current title holder. (Or, if the oldest son predeceases his father but fathers a son of his own before he dies, that grandson would be the heir apparent.)
An heir presumptive is the person who will inherit a title as long as he isn't displaced by the birth of an heir apparent. Generally speaking, a peer who has no legitimate sons has some other relative--a brother, a nephew, or cousin--who'd inherit the title if he died. Note that this heir must be a legitimate descendant in the direct male line of the original title holder (titles that can be passed through daughters exist, but are very much the exception rather than the rule). If there aren't any left, the title becomes extinct. An heir presumptive can't become an heir apparent even if it's certain the current title holder will never father more children--say, if he's elderly, senile, and impotent. For all the law knows, he might make a miraculous recovery and marry a younger woman who'd then give birth to a son displacing the heir presumptive.