Both concepts have to do with what a text has to offer as compared to how you read a text ( feminist criticism for instance is a way of reading a text). Deconstruction originates in the 60s with Jaques Derrida's work Grammatology. While Derrida never gives a precise definition of Deconstruction, he argues that it is impossible to pinpoint the meaning of a text because the text is full of internal contradictions. This does not mean that characters contradict themselves, but rather that a text is structured in a way that does not permit closure for a reader because it is not a discrete whole.
Structuralism had already been in use when Derrida wrote and it influenced his thinking. Structuralism originates with the thinking of Ferdinand de Saussure who is considered the first semiotician. But the foundational work of Structuralism was done by the Formalist School in Russia, the Prague School and in France by Roland Barthes. There are other adherents though. Structuralism derives from an attempt to give literary criticism a more scientific mode of looking at a text.While it can be understood to be an intellectual movement, in terms of literary analysis it means that a text reflects cultural structure, which in turn is modeled on language. Hence, a text is reflective of the culture it was produced in. Later on, Marxist critics would make use of this idea and begin to argue that a text is reflective of ideology.
Structuralism is very specific and formulaic at times, forcing close engagement with a text. Hope this helps.