Derrida originally used the word deconstruction in Of Grammatology as a way of translating Heidegger’s term Destruktion. Nevertheless Derrida’s deconstruction can definitely be distinguished from Heidegger’s. In both cases, the first idea one must dismiss is the facile notion which has nonetheless become prevalent that either thinker was attempting to “destroy” the philosophical tradition. Something much more subtle is at work here.
Heidegger introduced Destruktion to respond to the essential historicity of Dasein. Dasein is that on the basis of which the humanity of the human being is to be re-imagined (in other words, Heidegger reinterprets the being of human beings, and names it Dasein to distinguish it from the traditional interpretation), and its essential historicity is a recognition that Dasein never has immediate access to essences, but rather whenever and wherever it exists this access is inevitably mediated by tradition.
Destruktion grows out of Heidegger’s fundamental concern with phenomenology. Phenomenology re-introduced the idea of essential insight into philosophy - in other words, one cannot understand what time is, or even what Aristotle meant by chronos, merely by reciting his definition of it - one must rather have an intuition of time. By extension, the texts of philosophy offer an account of each philosopher’s wrestling with these fundamental intuitions, and one’s reading of philosophy must recover that basic insight. This essential insight represents the essentialism of Husserlian phenomenology. In contrast Heidegger’s thought could be called existentialism only if we keep this context in mind, and distinguish his thought from anything Sartre might have offered under that title. Though animated by the demand for essential insight, Heidegger nonetheless recognizes that we only have access to these essences by means of the very tradition which obscures them if it is treated dogmatically. The idea a contemporary German has of time can only be gained on the basis of his language and culture, which has its roots (says Heidegger) in ancient Greek language and thought. Thus to understand any of the basic terms which are foundational to thought and philosophy (truth, reason, being, etc.) we must return to the thinkers and the language which originally gave them the meaning we have inherited.
This can not be done by a simple leap, say, by picking up a translation of Parmenides. One must work backwards through each of the layers of the tradition in order to free oneself of the continual distortions the tradition has perpetrated, and only then may one understand in its simplicity and profundity the words of the ancient Greek thinkers. This process of gradually working backwards through the distortions of past philosophers is Destruktion. As one can see it does not at all mean that we are doing away with the tradition and creating something else, but rather that we are returning to its origins. Heidegger often uses the term Abbauen as a synonym for Destruktion, and both terms might better be described as a kind of dismantling, where we are examining and preserving the parts of the edifice, rather than annihilating them.
As a final note on Destruktion, I will add that this process is not turned exclusively towards the past but contains a strong futural component. It is out of our openness to our own future and its demands that the meaning of these past texts returns to us - they never become rigidified as they would in a textbook of philosophy. “Anaximander’s Fragment” (anthologized in both Early Greek Thinking and Off the Beaten Track) is an excellent source for pursuing these themes, as well as the introduction to Being and Time. Many of Heidegger’s lectures are relevant as well - Introduction to Phenomenological Research would be another good starting point.
In a word, the distinction of Derrida’s deconstruction is the recognition that Destruktion too can only ever reach an arbitrary stopping point, conditioned by accidents of historical transmission. There is nothing absolute about the idea that so-called western culture originated in ancient Greece, and the thinkers Heidegger returns to again and again themselves had multiple traditions and languages out of which their thought developed, much of which is lost to history. When we reach the bottom of our history we do not uncover a foundational origin, in immediate contact with the phenomena themselves, but rather a contingent limit to our further historical inquiry. In “White Mythology”, an essay in Margins - of Philosophy Derrida refers to what occurs at this limit with the rhetorical figure of catachresis. Catachresis occurs when a word is applied outside of its proper realm of meaning, such as in Gertrude Stein’s “As a Wife has a Cow: A Love Story”, in which cow is used to refer to a woman’s orgasm. Derrida is saying that the kind of essential insight Heidegger sought to recapture through Destruktion is ultimately impossible even through these means, because at the bottom of history we find a language and thought which is still arbitrary and contingent.
Derrida still affirms the necessity of something like Destruktion to the project of philosophy, and one sees him throughout his work tracing the development of different philosophical ideas. (in this he too is not a destroyer of the philosophical tradition - the French word is much closer in meaning to something like the dismantling I described earlier) He is always open, however, to the possibility that these concatenations are arbitrary and their connections only in the mind of the beholder, because of the necessary absence of any fundamental ground.
It is in Derrida’s “Letter to a Japanese Friend” (in Psyche: Inventions of the Other Vol. 2) that he recounts the life of this word. There are also a number of interviews in Points… which cover similar terrain. I would also recommend looking at “Ousia and gramme: Note on a Note in Being and Time” in Margins - Of Philosophy and the short book Aporias to better understand how to distinguish Derrida’s and Heidegger’s thought.
I would caution against using the word “critical” when describing deconstruction. Derrida always points out that deconstruction is opposed to criticism which, like its Greek root krinein, refers to the separating and distinguishing of meanings, while deconstruction is always open as well to the possibility of dissemination, the possibility that a text is ironic or animated by no intention-to-signify whatsoever. Your description of the relation of deconstruction to binary thought is accurate - deconstruction is a non-positional discourse. One does not say that something is good or bad, true or false, when one deconstructs, but rather shows how both positions are similarly unstable and untenable.
Deconstruction is definitely not the application of Destruktion to a limited field of inquiry, such as the text, which you mention in your question. First of all, textuality is not regional for Derrida. It refers to what he time and again calls generalized writing, which is what we arrive at when the traditional concept of writing is deconstructed. We find that the predicates an entire history sought to aver of writing (thus seeking to preserve speech from their contagion - predicates such as absence from the origin, being a copy of a copy, the potential of misinterpretation, etc.) are actually true of everything - everything can have a meaning or be interpreted and thus these predicates apply to everything equally. If we think of this as meaning that everything is a text in the sense of words on a page then we are still trapped within the traditional definition - Derrida is showing us that textuality cannot be contained within such limits. It would be more accurate to see Derrida’s deconstruction as more capacious than Heidegger’s - it reaches the bottom of the latter’s thought and finds - no bottom there.
