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a table organizing the input rule output of a function
If it is boolean logic, typically that is called a Truth Table.
It is generally referred to as "a table of values"
if there is an = sign
When you see the actual function (e.g. f(x) = ...) you can know what each input corresponds to, and can construct any table. If you are given just the table, you cannot always predict the function correctly, since the function the table seems to represent does not necessarily have to be that function. For example, it might seem that x : f(x) -2 -4 -1 -2 0 0 1 2 2 4 would correspond to f(x) = 2x, but this is not necessarily the case. There could be some arbitrary function that just happens to contain those five points.