[moate]

You take money that would have ostensibly gone to the citizens of Tokyo and instead provide it to the citizens of town of your choice.

Reallocation and redistribution are synonymous here, one is just used in more headlines (probably because more people use "distribute" more regularly than "allocate"). Nothing different should be inferred by either word choice IMO.

[themaninthedark]

I think that there is a bit of distinction.

Reallocate says that you are changing where the money is going

Redistribute says that you are collecting money then parceling it out.