My guess is that finite 9 means the set of 9 digits {0 1 2 3 4 5 6 7 8}. All arithmetic operations need to result in one of these digits. There is no meaning to negative numbers. The easiest way to think of how to deal with this is to think of remainders. If we divide a number by 9, we get a quotient and remainder. The remainder will always be between 0 and 8. For example, 17/9 would have a remainder 8, and so would 26 and 35, and so on. These numbers are in intervals of 9, so let's work backwards. 8 has a remainder 8, and -1 also has a remainder of 8, as do -10, -19, etc. So a negative number is converted into a number between 0 and 8 by simply adding 9 until the result becomes positive.
To answer the question, then, 5-8=-3, now add 9 and we get 6 so 5-8=6. In this context mod 9 or modulo 9 would be the same as finite 9.
I hope this helps.