In the literature the terms Randomization and Permutation are used interchangeably. With many authors stating "Permutation (aka randomization) tests", or vice versa.
At best I believe the difference is subtle, and it lies in their assumptions about the data and potential conclusions which can be drawn. I just need to check whether my understanding is correct, or whether there is a deeper difference that I am missing.
Permutation tests assume that the data is sampled randomly from an underlying population distribution (the population model). This means that the conclusions drawn from the permutation test are generally applicable to other data from the population .
Randomization tests (randomization model) "permit us to drop the implausible assumption of typical psychological research—random sampling from a specified distribution" . However that means that the conclusions drawn are only applicable to the samples used in the test .
Surely though, the difference is only in terms of the definition of population. If we define the population to be 'all patients with the ailment and are suitable for treatment' then the permutation test is valid for that population. But because we've restricted the population to those which are suitable for treatment, it is really a randomization test.
 Philip Good, Permutation Tests: A practical guide to resampling methods for testing hypotheses.
 Eugene Edgington and Patric Onghena, Randomization tests.
 Michael Ernst, Permutation Methods: A basis for exact inference