If you will notice you have -2-2 not -2^2 = -4 on your calculator Raccoon.
the second 0-2^2 becomes 0-(2^2) because the minus sign is an operator.
And in -(2^2) well the - is applied after the exponent is worked out.
but in the case of just -2^2 it is not a minus operator but infact signifying it as a negitive number. the +/- button makes it -2^2 become (-2)^2 invisibly because minus was not used but a negitive to the base number.
But in the end yes in mIRC and programming that don't have +/- to signifiy the number/base as negitive it is in fact a minus so -2^2 = -4, But calcaulators -2(negative two) is the same as (-2) when programming.
[+/-]  [^]  [=] 4
[-] [ 2] [^]  [=] -4