Is there any different between function and relation

A function is a special kind of relation.

Relations pair up x and y coordinates, either by listing them or by writing an equation.

Functions have the additional property that no two values of y have the same value of x.

Yes. In a relation the numbers have a relationship though the use of a domain and range. In a function, there is a specific set of numbers and you would only get one range. All functions are relations but not all relations are functions.