They are essentially the same. The names are different because they are defined in different contexts. The idea behind each is that they accept a vector of parameters, end either return a vector (or matrix) that can be compared to external data (objective function in a curve-fitting sense) or do the comparison themselves internally and return a value that indicates how well the parameters approximate the desired solution.
As the result, the syntax may differ slightly to be appropriate to the specific application, but the idea behind both objective functions and fitness functions is the same.
