Well of course the answer is that you can use whatever you like. But the question should be is it the same?
No, CalciDust isn't just chalk.
Strictly speaking chalk is mainly calcium carbonate, but it can contain other things such as silt and clay which bring in other elements.
The term chalk' isn't scientific and is used for other things, e.g. sticks of chalk for blackboards are calcium sulphate, industrial chalk may contain calcium sulphate or calcium oxide. Sports chalk used in sports often isn’t even calcium, its frequently all titanium dioxide.
The point is that 'chalk' is a loose term which means different things, many of the compounds can’t become part of an equilibrium in the body and so can’t be absorbed - i.e. chalk in chalk out.
Calcium and chalk is simply not just what people think it is.
Buying ‘powdered chalk' two days running could get you two different things because functionally chalk depended where you buy it and what its sold for, it isn’t a food ingredient.