How does Hamlet think he is different from the actor?

Answer 1

You are probably alluding to Hamlet's soliloquy "Oh, what a rogue and peasant slave am I" in which Hamlet says

• Is it not monstrous that this player here,
  But in a fiction, in a dream of passion,
  Could force his soul so to his own conceit
  That from her working all his visage wann'd,
  Tears in his eyes, distraction in's aspect,
  A broken voice, and his whole function suiting
  With forms to his conceit?

He then goes on to say,

• What would he do,
  Had he the motive and the cue for passion
  That I have? He would drown the stage with tears . . .

Hamlet is thinking about the actor's ability to express himself, to act in a way which shows his emotions, even though they are fictitious emotions. Hamlet thinks he cannot do this, that he is a "dull and muddy-mettled rascal" who can "say nothing". This is, of course, ridiculous, because Hamlet does nothing but talk. He talks more than any other Shakespearean character. Ironically in this soliloquy in which he says he can say nothing, he goes on and on. In the next scene he will tell Horatio, "give me that man who is not passion's slave" and will admire him for the exact opposite qualities than those he finds in the player.

Answer 2

Because the actor showed more emotions than the other actors.