Scala is a great language with a rich excursion into type system design (and other things). Pyret is designed to reinforce specification (more general than types) and to do so through a combination of static and dynamic means. That much I've already said.
Let me point to testing as an example of where we differ. Testing is really important to us. As you've seen, we have lightweight, in-place test cases. In addition:
1. We have a growing family of language support for writing tests well (e.g., see "satisfies" on the Pyret home page). I expect this to grow richer and richer.
2. We are working on some interesting ideas about the scope of testing blocks. We don't say this on the home page, but you can also write "test" blocks for data definitions, not only for functions. But now the functions that operate over those data are going to want to use instances of the data. We're working on a "scope conduit" to take definitions from the data definition to its functions.
3. As some readers have noted, in most languages, you simply cannot write unit tests for a function nested inside another, because you can't even name it. In Pyret, because definitions can include tests, this creates no problem at all.
4. We are now working on a type-inference approach that uses tests, rather than code, to infer types. The code is then checked against these inferred types.
Essentially, testing is a kind of metaprogramming, and metaprogramming works best when you integrate it into the language (what Racket has shown) rather than as ad hoc external tools. Each of the above four examples is really just a specific instance of this general issue. Since testing is an especially important form of (dynamic) metaprogramming, integrating it well into the language from the very beginning is likely to lead to expressiveness, flexibility, and cleanliness that may be harder to achieve from the outside.
This is part of a more general philosophy. To me, testing is a form of _specification_, and we want to see rich descriptions of program invariants expressed with a gentle blending of static and dynamic methods. We don't want to be so grandiose as to call Pyret a "testing-oriented" programming language, but in our minds it is, with testing having both the base role of making sure we (as programmers) didn't screw up but also the exalted role of providing an alternate, independent description of the program we're trying to write. (This is something I emphasize a lot in my teaching: eg, http://cs.brown.edu/courses/cs019/2012/assignments/sortacle, http://cs.brown.edu/courses/cs019/2012/assignments/oracle).
This is a philosophical position, and so hard to quantify through individual bits of code, but I already see small influences of this (as above) and I expect it to guide us to a very different point in the design space over time. It feels safe to say this is quite different from Scala's viewpoint.