It seems Wolfram Alpha appropriately excludes March 11th for the math folks (e.g. kind of like SQL BETWEEN, syntax convenience, etc) and Bard appropriately includes January 11th and March 11th, as that is how it would be commonly interpreted.

Edit: or not, March 11th is not a weekday. Though I count 43 weekdays including Jan 11th, so perhaps Wolfram is using an open interval while bard is using a closed interval.

How many days are between Sunday and Saturday of this week (I live in a place where weeks are generally seen to start on Sunday and end on Saturday)?

Five, right? Would you say seven?

Guess I must be a "math folk."

No, I would say 6.

How many days are there between today and tomorrow?

By definition, there is exactly 1 (one) day. That's what tomorrow means :)

Your math would say zero.

Which day is between today (Thursday) and tomorrow (Friday)?

There are no days between today and tomorrow. No things _between_ this thing and the next thing.

I find your mathematics pretty confusing.

In most contexts for time differences, a "day" is a time interval (24 hours) instead of a "concrete thing".

If my job contract says that there has to be "one day between" my resignation letter and my handing back my badge, then it means I can resign on Monday and give back the badge on Tuesday (the next day ; "one day after" ; because "one day" has elapsed). Not Monday/Wednesday. Otherwise "zero days between" these events would mean Monday/Tuesday (with your math) and Monday/Monday is also zero?

But I guess we're just rehashing the old argument on whether indexes should start at zero.

Small nit: BETWEEN is boundary inclusive, testing membership within a closed interval (at least in all SQL dialects I’ve used)