Do these variations mean anything different, or is one more correct?
I have been accepted onto a course at the University of Stack Exchange
I have been accepted to the Masters programme
Are there any other variations?
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"Accepted into a course" is the usual wording for these things.
Accepted into a course is American English. Accepted onto a course is more common in British English.
Into or to would be correct for both, with into the more usual in both cases.
At or to for "...accepted at the University...".