Invisalign refinement trays versus Invisalign additional aligners?

Those terms are referring to the same thing, all this means
is that more treatment is needed beyond the initial set of trays. The number of
new aligners can be very different and can certainly be more then initial aligner
depending on how your dentist times the movement and what they are trying to achieve.

The additional aligner refers to the extra aligners after the initial set was sent.They could be part of a mid-course correction or part of the refinement process.  Teeth sometimes don't always move the way we expect or forsee. Some movements require additional time to achieve. You can ask your dentist what teeth didn't move as expected and what the refinement process will do.  This should make it clear what your dentist is trying to achieve and account for the longer treatment. Hope this helps.  Good Luck!