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rhb
You're missing what a date value really is: a count of days elapsed since 31 Dec 1899. And using MONTH was causing your problem.
Right now TODAY() = 45352 (as you'll see if you format as number)
MONTH(TODAY())-1 is equivalent to (current month) -1
MONTH(TODAY()-1) is equivalent to yesterday's month
They'll only give the same result on the first of a month Feb-Dec.