Accomplishment vs. Achievement (implicit superiority)
I elsewhere saw the difference between the two explained thusly: accomplished denoted "completed for someone else's benefit", achieved "completed by oneself". I consider it a one off, but can anyone confirm if there is an implicit superiority in language usage. This would be useful in the positive sense one would say "... an accomplished career".
Solution 1:
I think you are right to be wondering if there is a difference, since in my experience (UK English, mostly academic) the two stem-words seem to be used interchangeably to mean much the same thing. If there is a shade of difference in meaning or usage, I guess that accomplish(ed) refers more to polish and style, and achieve(ment) more to overcoming difficulty. Otherwise they both mean to get something done - and finished. I wonder if the poser of the question would like to say whether it is UK- or US- or other English usage that is of greatest interest?
Solution 2:
I would say that one would accomplish a task and achieve a goal or target. There is considerable overlap between the two.
Solution 3:
Accomplishment is getting things done, while achievement is getting things done right.