Intertextuality is very widespread
It's from the work of Mikhail Bakhtin that we learned something fundamental: whenever we open our mouths, they are filled with the words of others. We continuously use and re-use elements of discourse borrowed from earlier moments of usage. Such forms of intertextual re-use can be explicit, e.g. whenever we quote someone's words or use references in academic writings. They can also be implicit, whenever we borrow and deploy particular patterns of discourse that have their origins elsewhere. For obvious reasons, implicit intertextuality is much more widespread than explicit intertextuality, for we tend to draw on socially and culturally conventional frames and formats whenever we find ourselves in particular communicative situations. This will become clear when we turn to some related terms.
Interdiscursivity and entextualization
Norman Fairclough coined the term 'interdiscursivity' for implicit forms of intertextuality, while he preferred to use 'intertextuality' for explicit acts of borrowing and reiteration. Interdiscursivity, in his approach, pointed towards the widespread influence of dominant discourses, such as e.g. neoliberal discourses on the economy and the labor market that are reiterated as large frames in millions of individual examples. This is a useful distinction, but it is important to see that the distinction between explicit and implicit intertextuality are different sides of the same coin.
Michael Silverstein and others proposed the term 'entextualization' to point towards something that defines all forms of intertextuality: the fact that, whenever we use the words of others, we never merely repeat them, but we redeploy them in an entirely new context and create different meaning effects with them - we transform its indexicality, we indexically change words while repeating them. For instance, when we quote a prominent author in a paper, the quote is extracted from its original context (as an element in an argument made by the original author) and redeployed as an element in our own argument. Which is why things that were a mere detail in the original author's work can be turned into a major point in our own papers and vice versa.
The point made by the term 'entextualization' is that intertextuality never leads to identical texts, but changes the material we re-use. Even when it looks as if we merely 'repeat' something - think of someone saying "I love you, I love you, I love you" - the repeated phrases are not identical, because repetition itself changes something - it adds emphasis, importance, relevance to the phrase.
Heteroglossia and polyphony
Bakhtin himself used the term "heteroglossia" to point to the fact that every piece of discourse is made up of various "voices", each of which points to different origins. For instance, many of us talk about what we call "the news" by means of things we got from the mass media. According to Bakhtin, we thus incorporate the voice of the mass media into our own statements - a form of implicit intertextuality, if you wish. It is even clearer when we quote someone else in a conversation (like in "...and then Maggie said 'wooah, I'm like not su sure about it' and then we all started laughing"). When we do this, we often change the tone of voice, the intonation, the rhythm of pronunciation and even the accent - pretty well imitating the quoted speaker's voice.
A very similar idea was expressed by the term "polyphony" in the work of Oswald Ducrot and other (mainly French) discourse theorists. Like in music, polyphony in discourse stands for the occurrence of different voices in the same discursive action. The example of Maggie given above can serve as an illustration here, too.