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Domain Driven Design (DDD) is a way of thinking and communicating about the problems and its solutions.
Domain Specific Language (DSL) is a way of writing code.
They're similar because they both start with the word "domain". That's it, I guess. :-)
The differences, one is an approach to building systems using a Domain Specific Language language (DSL) instead of a General Purpose Language and the other is an architectural approach (DDD) to designing and building systems.
The similarity is that they both focus on the specific domain.