By saying that he is not Prince Hamlet and was not meant to be Hamlet, Prufrock is, of course, making us think of how he is, in his indecision, similar to Hamlet, as in the experiment in which someone tells you "Do not think of a rhinoceros," and even if you had no thoughts of the rhinoceros, you now can think of nothing else.
The main distinction Prufrock makes between himself and Hamlet is not of type but of importance. Hamlet was a heroic character of a heroic age, caught between decisions which affected all of Denmark. By contrast, Prufrock is a mere "attendant lord" asking the trivial questions of the modern age. He worries about whether to eat a peach and how to wear is trousers, and is concerned that the servants are laughing at him.