How each subset is counted. The dot matrix is identical in every mode — the dots fix which sets a column represents (its degree). mode only changes how the bar height for that column is counted.
"distinct" counts elements in exactly those sets and no others (the classic exclusive intersection — columns are mutually exclusive, so bars sum to the total). "intersect" counts elements in at least those sets, i.e. the full |A ∩ B| including elements also in other sets. "union" counts elements in at least one, i.e. |A ∪ B|. The two inclusive modes overlap, so their bars do not sum to the total.
Worked example. Say 84 elements are in A and B only, and 40 more are in A, B, and C. The A & B column (degree 2) shows 84 in distinct mode, but 124 (84 + 40) in intersect mode — same column, different count.