Can you explain with example ?
sequence = [5 6 3 2 4 5 6 7];

nth
if I do partial_sort with n = 4, the elements 0,..,4 (before and
including position n) will be sorted, the 5,..,7 will not be
necessarily, that is, a possible outcome is:
[2 3 4 5 5 6 7 6]

nth
if I do nth_element, not even the elements strictly before position n
will be sorted, but they will be all less or equal to the nth. A
possible outcome is:
[2 4 5 3 5 6 7 6]

nth
If you have fullsort, every element is in its "sorted" position. If you
have partial sort, the first n elements will be in their sorted
position. If you have nth_element, only the nth element is in its sorted
position.
Best wishes,
Zeppe