Statistical generalisation stems from analyses that are conducted on data (from a sample) to the whole population, whereas analytical generalisation extends conclusions based on theory without any involvement of data analysis.
I agree with previous definitions. I would add that, from an epistemological point of view, you may (if you do the right thing) be on a firmer ground when doing statistical generalization than doing analytical generalization.
The reason is simple: there exist a series of statistical tests to look at the quality of the estimates when expanding the results of a survey, starting with the random selection of the sample.
It is much more difficult to do the same when pooling together case studies and expanding the observed results to the entire population. Unless some additional control are applied, the observations belong to the set of case studies and cannot be generalised without taking a serious risk.
This said, a relatively new branch of social science tries to develop formal quality checks on social cases by introducing randomized experiments. A fascinating subject, indeed. The objective is to close the gap between statistical surveys and case studies by providing randomised control groups. So, stylised facts extracted from case studies can be check for robustness in (almost) the same way than statistical sample surveys.