[wongarsu]

Imagine you start with one unique solved grid. There's 81 numbers, so by just removing one entry you arguably have 81 different "puzzles" that all lead to the same unique solution. From all of these you can also remove any second number, and get another 6480 puzzles that will still all have the same unique solution.

Now imagine taking away 61 numbers from the solved puzzle to get a sudoku with 20 starting numbers. Some of those puzzles have to be discarded because they might lead to multiple possible solutions, but you will still be left with millions of possible puzzles that look distinct to a human, and require different strategies to solve, all leading to the same solved grid.

[dougSF70]

In theory yes, but layouts that require just filling in missing numbers are not puzzles. The layouts with missing numbers become puzzles when some thought must go into entry selection. The question is how many puzzles requiring logical deductions are there for each unique 81*81 grid.

[wongarsu]

At first approximation, the number of logical deductions just goes up (exponentially?) with the number of missing digits. That's why you see many sudoku books grouping puzzles by "difficulty" by just stating how many digits are given.

Of course humans can make much more interesting puzzles, where you are expected to make a certain string of logical deductions to reach the solution. But simple "machine-made" sudokus seems to sell well enough, so I see no reason to exclude them from the definition.