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I know they can be used interchangeably, but in the spirit of structuralism, what are the differences between them?
From Postmodernism - Wikipedia, I think that postmodernism and post-structuralism are basically the same, and are used when you want to talk about the movement in philosophy, and deconstruction is only used when you analyse a text. Is this understanding correct?
tl;dr - deconstruction is something specific (usually from Derrida less commonly from Heidegger). Post-structuralism is a near synonym for late 20th century French philosophy and is a type of "post-modernism." Post-modernism is a term which means anything after modernity -- no idea what it means without context.
Postmodernism is a grab bag term that applies to many different things that come ... after modernism. It's hard to know what someone means when they say this term as it gets bantered about (usually by people who are opposed to something they call "postmodernism" or by people who thinks it's the best thing ever). One reason it's hard is that what is modernism is not as easy to answer as it appears. In general, in philosophy, modernism refers to the period from Descartes and Locke down to the period of Kant ... and maybe Hegel, and further maybe Kierkegaard, and Nietzsche (depending on the speaker and their interpretations of these philosophers).
Post-structuralism is one of the things that comes after modernism. The name "post-structuralism" gives it a firmer meaning than "post-modernism" and locates it within a French tradition. It's in many ways quite similar to the project of structuralism. Structuralism is a project that says meaning exists in systems ("structures") not in sentences or individuals. Post-structuralists keep the structures but often drop out the idea that there are meanings beneath this that could be found or could exist. It's hard to articulate quite what they mean by this (because part of their point is to attack both "they" and "mean"), but the basic idea is that our naive concept of things where speakers are subjects that have wills, intentions, thoughts, and values is wrong and what's actually happening is that ideas move in their own force.
For this reason, it's not really clear if the people called post-structuralists (e.g., Foucault, Lacan, Butler, Kristeva, Derrida, and others) are engaged in a fundamentally different project or just an extension of the original structuralist agenda. This is because they accept the main point of the structuralists -- that the structures are primary; they reject or possibly amplify the structuralists diminishing of the subject. (How exactly and what exactly will vary depending on who we are talking about).
Deconstruction is a term for a method that appears originally (not necessarily meaning "first" but meaning as the origin of the method) in Heidegger that refers to showing how the concepts we have doesn't work the way we often think they do (see this answer). For Heidegger, Destruktion (unlike it's English counterpart destruction) means both a tearing down of the old and a building up of the new (SEP; n.b. my German is not good enough to judge whether Heidegger's usage of the term is normal or singular). Derrida is probably most famous for this both as a method and as a name for a type of post-structuralism. Derrida also uses the term Bricolage for the same basic idea with the meaning that when we tear down concepts we think are clear, we will discover they are not so clear. The wikipedia articles in English and German are helpful here.
One thing that muddles things even more is that the definitions I'm giving you above are some light off-the-cuff definitions coming from philosophy. Post-modernism also refers to a movement in art and architecture that has some ideological overlap. And the usage of these terms in literary criticism is non-identical (note I didn't say completely different).
In her essay on Post-Modernism, Linda Hutcheon states that "Poststructuralist discourse paradoxically contests, yet unavoidably inscribes, the very preconceptions it seeks to challenge." in her A poetics of postmodernism(55) From what I gathered in literary theory, and correct me if I'm wrong Post-structuralism in its attempt to deconstruct structure, it falls into the trap of being structural itself as it took the other position For Hutcheon, Post-Modernism affirms both, challenges both and revels in its own contradictions answering question by questions as she adds to correct Lyotard's definition of postmodernism "Let us inscribe and then challenge totality; let us (re)present the un(re)presentable; let us activate differences and admit that we thus create the honor of the name and the name itself.”
To put it in very bare terms, Postmodernism is a way of being, a socio-cultural practice, whereas, Poststructuralism is a way of knowledge, a academic practice. And Deconstruction is a way that poststructuralist philosophy functions using the slippage of meaning as its base to question existing linguistic structure and the values and consequent power, considered inherent in language.
I would demarcate them as follows:
These categories are mostly descriptive, few philosophers we would characterize as "post-structuralist" identified themself with this name.
