Online Merriam-Webster provides some information of the subtle differences between STOP and DISCONTINUE.
STOP applies to action or progress or to what is operating or progressing and may imply suddenness or definiteness
DISCONTINUE applies to the stopping of an accustomed activity or practice
It appears that the subtlety lies in
(a) Stop being a generic, all inclusive term used for actions to cease to exist, while
(b) discontinue applied (only) to an ongoing/accustomed "event"
However, I recently came across an announcement from a pharmaceutical company that reads
"We are stopping the study, not discontinuing it"
It is not clear to me what this announcement tried to emphasize. The following two seem identical to me
(a) we are stopping the study
(b) we are discontinuing the study
while (c) we are stopping the study, not discontinuing it
feels slightly different, although I don't know exactly how to verbalize the feeling.
Also, does the following sentence make "sense" - (d) we are stopping the study and discontinuing it