1/ I wanted to know what's the difference between the above three definitions. As per my understanding, "fun1" and "fun2" look the same, taking one integer and returning two columns with multiple rows.
Yes.
Can the above definition (used for fun1 and fun2) cover both single and multiple row scenarios.
In so far as one is a valid number of rows to return from a function that returns zero or more rows, yes. But if the function is incapable of returning more than one result it should not be marked with table/setof on semantic grounds.
2/ How does someone decide which type of definition is to be used?
Between 1 and 2 is a style choice. I prefer TABLE. Using setof is more useful when the returned type is predefined. Or a true record where the caller has to specify the shape.
For 3, having a non-set-returning-function that outputs multiple columns is just odd, IMO. Personally I'd go for pre-defining a composite type, then return that type.
