I can address the British peerage system; others may vary.
The basic concept is called a 'Courtesy Title'.
A peer of the rank of Earl, Marquess, or Duke frequently has secondary (lesser) titles; for example, one could be the Duke of A and also the Earl of B and Viscount of C. Typically, the eldest son is granted the 'courtesy title' of address by one of the lesser titles; the eldest son of the eldest son might be granted the next 'courtesy title'. In our example, then, we'd have the Duke of A, his eldest son would be the Earl of B, and the eldest grandson might be addressed as the Viscount of C.
All other sons, daughters, grandsons, or granddaughters of the peer would receive the courtesy title 'Lord' or 'Lady', so, for example the youngest son of our Duke above would by called 'Lord'. This title would also apply to the eldest son of a peer with only a single title (as in the case of Lord Byron.)
In conversation, 'the dukal heir' is correct, but it is not a formal title.