They're actually quite similar. Docker is to lightweight containers as Vagrant is to virtual machines (more or less anyway; Vagrant lets you configure a lot more at this point). The nice thing is that the Dockerfile makes the whole thing a lot more transparent; VMs are sort of nebulous black boxes, whereas you can follow the construction of the container through the Dockerfile.

I'll be interested in seeing how the ecosystem evolves when Vagrant becomes better able to manage containers.