The difference between burnination and disambiguation was larger in the older times when Stack Overflow staff were involved. Burnination meant that the staff used to delete the tag as a whole. Disambiguations or retag requests were something which the users were doing it themselves by going through all the posts and selectively changing the tag. That said, there still are a few differences between burninations, disambiguations and retag requests.
- Burnination requests are when the tag itself is inherently harmful. It usually ends up with the tag being completely removed from all the posts. The focus is more onclosing and deleting the off-topic questions. If there are lots of questions, Stack Overflow staff will usually delete the tag as a whole (a throwback to the previous times)
- Disambiguation requests are more focused on making the tag's meaning clear, and creating new tags in order to retag those that are not necessarily about that particular tag. The tag stays as is at the end, or perhaps renamed to a more meaningful name. (If the answer to question 2 of the burnination request is "yes", while the remaining is "no", then disambiguation is the route)
- Retag requests are ideally about automatic retagging of questions, or atleast automatic-like retagging of questions. These include tag merges, where the synonym tag is completely retagged to the new target tag, and renames where the questions with the old tag are retagged to the new tag. Here we usually go through search queries to find out which all questions need to be retagged.
I agree that the difference isn't as clear as day, and I don't really mind much about the nomenclature as long as the result is towards the overall good for the site.