It's pretty common to see the term "DSL" crop up in the context of MDSD. Indeed some MDSD people seem to think that DSLs only exist within the MDSD world. I've been writing a lot on DSLs recently for my book, but so far I haven't really touched on the MDSD angle much Instead I've concentrated on DSLs role in more conventional programming. DSLs exist in both the textual language and MDSD worlds and play pretty much the same role for both.
In an MDSD context DSLs are again a language targeted at a specific kind of problem as opposed to general purpose languages such as the UML. As a result they can have the same kind of relationship: build a system in the general purpose modeling language and use DSLs for various specific aspects. Since MDSD hasn't caught on that much, however, you also see a different approach where modeling DSLs are used in the context of a traditional language environment. Here you might use several modeling DSLs that generate Java code to be combined in a Java project. In this case there's no general purpose MDSD model around - you use MDSD for each DSL relatively independently.
In order to use model-oriented DSLs you need a different, ProjectionalEditing, approach to tooling. This introduces quite a few pragmatic issues as the general support environment for such tools is less established. In order to define your own DSLs you need more specialized tooling - something I call a Language Workbench.
DSLs seem to have a proportionately higher emphasis in the MDSD world than they do in the mainstream programming world. Cynics think this is a result of the MDSD community desperately searching for a way to remain relevant, fans of MDSD regard it as a sign of MDSD's superior sophistication. I think this is mainly due to the fact that the MDSD community is smaller and has far less in the form of established practice.
A particularly visible sub-community of MDSD is centered around ModelDrivenArchitecture (MDA). I'm not much of a fan of MDA in particular, but am particularly skeptical of MDA DSLs.
There is much that model-oriented DSLs share with textual DSLs. I put a lot of emphasis with textual DSLs in basing work around a Semantic Model. MDSD, as its name indicates, is very much about driving a system from that kind of a model. A difference is that most MDSD people assume that you'll want to generate code from that model rather than executing the model directly.
As I write this, I'm not sure how much I'm going to cover language workbenches in my book. Certainly I'll at least discuss the overall concept behind them, but the coverage may not be that deep. This will be partly due to the large amount of material I seem to be generating on textual DSLs and partly due to the fact that language workbenches are much newer and thus more volatile and less mature.