Rows, columns and regions can be collectively referred to as groups, of which the grid has 27.
The One Rule encapsulates the three prime rules, i.e. each digit (or number) can occur only once in each row, column, and box; and can be compactly stated as: "Each digit appears once in each group."
Other variations include additional value placement constraints, alternate symbols (e.g. letters), alternate mechanism for expressing the clues, and compositions with overlapping grids.
Sudokus variants can also have additional constraints on the placement of digits, such as "< >" relations, sums, linked cells, etc.
The meanings of most of these terms can be extended to region shapes other than boxes (square-shaped).