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This paper deals with the maximum value of the difference between the determining
number and the metric dimension of a graph as a function of its order. Our technique
requires to use locating-dominating sets, and perform an independent study on other
functions related to these sets. Thus, we obtain lower and upper bounds on all these
functions by means of very diverse tools. Among them are some adequate constructions of
graphs, a variant of a classical result in graph domination and a polynomial time algorithm
that produces both distinguishing sets and determining sets. Further, we consider specific
families of graphs where the restrictions of these functions can be computed. To this end,
we utilize two well-known objects in graph theory: k-dominating sets and matchings
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