The move instruction copies a value from one register to another. The li instruction loads a specific numeric value into that register.
For the specific case of zero, you can use either the constant zero or the zero register to get that:
move $s0, $zero
li $s0, 0
There's no register that generates a value other than zero, though, so you'd have to use li if you wanted some other number, like:
li $s0, 12345678