They are different in the same way that subtraction of integers is different from their addition.
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Subtraction is not commutative nor associative.
Then you are adding two rational numbers with different signs! No big deal!
what is the rule in adding rational numbers
In subtraction you take away rather than add. Also, addition is commutative, subtraction is not so the order of the numbers does matter for subtraction.
There is only one type of rational number so there are no different types which you can add.