The question basically is how $300 - 61 \cdot 425 \bmod 880$ can turn into the value $775$, while a calculator returns a different value, likely $-105$. The difference is that sometimes a remainder is taken to have a value in the range $(-N, N)$ rather than $[0, N)$.
$300 - 61 \cdot 425 = -25625$. So you can say that we're trying to find a value $x \cdot 880 + y = -25625$. Now is can be $-29 \cdot 880 - 105 = -25625$ to find a value within $(-N, N)$, similar to finding $29 \cdot 880 + 105 = 25625$. $-105$ is then commonly called "the remainder"; it's what you would get if you would perform simple tail division yourself.
However, for cryptographic operations we generally try and perform operations in a group of order $N$ instead, with $N$ possible values in the range $[0, N)$. so in that case we can take $-30 \cdot 880 + 775 = -25625$, and the result will be $775$, exactly $880$ more than $-105$ in other words. This is commonly called taking the modulus, although this value can also be called a remainder.
So to find the right value within your calculator you can simply add $N = 880$ if the result is negative. A little trick in programming languages is to perform
((X % N) + N) % N, so that an
if statement can be avoided. Note though that the
+ N may cause an overflow for large values of $N$.