While, in one way, the letter is a fair statement of their differences it is quite misleading in another. For Heidegger certainly does not think that they agree about what must be called the “world”. That is more like the issues on which their differences rest. It is enough of an issue that Heidegger can, in Vom Wesen des Grundes does, argue that “the being in which the world is constituted” or Dasein, is rather of exactly the same nature as the world it constitutes. Which I to say, at the very least, that we should not think that it is clear what “world” means and unclear what “Dasein” means; we can be no clearer about one than we are about the other. Vom Wesen des Grundes, despite its title is largely concerned in the concept of “world”, and in particular with establishing the concepts linage---- a legitimate concern, since the ordinary meanings of the term and Heidegger’s are only oddly akin. The “world”, on his definition, is not “totality of things” but that in the terms of which we understand them, that which gives them measure and purpose and validity in our schemes. What leads Heidegger to offer the definition is not obvious, but it may well be related to explaining why we must, and no less how we can, share certain notions about the measure and purpose and validity of things. And presumably it is important to have the explanation because sometimes we do not, or do not seem to, share such notions.
When Heidegger talks about “world”, he will often appear to be talking about a pervasive interpretation or point of view which we bring to the things of the world. This, in any case, has been the view of many commentators. But there is little sense in speaking of “a point of view” here since precisely what Heidegger wants to indicate with the concept is that none other is possible. And there is no more sense in speaking of an interpretation when, instead of interpretation, the “world” is meant to be that which can keep us from seeing, or force us to see, that what we have is one. Heidegger’s concept is quite like Kierkegaard’s “sphere of existence” and Wittgenstein’s “form of life”, and, as with them, it enters his inquiry only at its limits, when a problem moves out of his depth or jurisdiction.