For me a sudoku consist of a grid of n times n cells, which is dissected into n regions of size n. Some cells may contain a number and the goal is to fill a single number into each cell, such that in every row, column and region, every number from 1 to n appears exactly once. (Less formally, this should be a description of what is called "Irregular Sudoku". In my oppinion a "Classic Sudoku" with square regions is just a popular special case of a sudoku.)
For me a variation of a sudoku (and this is something, that holds for variations of every other puzzle type too) is similar to a sudoku, but some (but not too many) constraints may be changed, that is
- Constraints may be removed (for example a Sudoku with penrose grid, like the one I created for the 24h in 2016: Download round 4)
- Constraints may be replaced (for example a Scattered Sudoku)
- Constraints may be added (for example a Greater-Than-Sudoku)
- For me a bare latin square is a sudoku (just make all regions rectangles of width 1).
- A Starbattle-Sudoku is a sudoku variant, as the constraint "digits from 1 to n" is replaced by "digits from 1 to n-2 and two stars"; and a new constraint "stars may not touch" is added.
- It's possible to have sudokus where symbols repeat. As far as I know, some people have the ability to spot missing numbers immediately, when all numbers have to be distinct, while this ability does not work anymore when symbols repeat. Other people (including me) do not have this ability. I don't think that this should be a reason to remove types from the variants lists. People who can spot missing numbers, should still be able to cope with puzzles, where they cannot use their special ability. In that case, they have to use other means and I think, that's fair.