Prof. Solum discusses vagueness vs. ambiguity, and the relationship between this distinction and the interpretation/construction decision, here.
I would characterize the difference in terms of linguistic architecture, as follows:
Ambiguity is what occurs when the sound or textual output matches more than one possible linguistic expression, where a linguistic expression includes a sound output, a meaning output, and the procedure that generates the pair of outputs. Ambiguity is the result of the fact that sounds and meanings do not perfectly correspond to one another.
Vagueness is what occurs when the meaning output of a linguistic expression, or a part thereof, corresponds to a concept (in our case, a legal concept) without clear boundaries. Vagueness is the result of the fact that our conceptual system is incomplete, so that it is not always known whether a certain object, for example, falls in a particular category. It is a necessary result in light of the fact that our conceptual system is discrete, while the world that it represents is often continuous.
The role of the interpreter/constructor in the case of an ambiguity is to select the appropriate meaning output in light of the sound output, using evidence such as the context in which the expression was generated, the likelihood that the meaning output was the one intended by the person or group articulating the linguistic expression, and the naturalness of the sound-meaning correspondence (a particular meaning can be possible but improbable, for example, if it presents great difficulty in linguistic processing).
The role of the interpreter/constructor in the case of vagueness is to modify the conceptual legal scheme so that it optimally covers the case at hand.
[edited for typos 1/17/2009]