There are two kinds of dreams: waking and sleeping, right? The waking kind of dream has a positive connotation: "I dream of Africa; I dream of genie..." It links the speaker with a goal. This is Claudius' use of the term. His dreams are political, materialistic. Before the play, he dreamt of the crown; he dreamt of having the queen for his wife. As the play begins, he has achieved both. His dreams are ambitious. And now he dreams of settling the score with Fortinbras in Norway. In Act.ii, Claudius addresses the state:
For all, our thanks.
Now follows, that you know, young Fortinbras,
Holding a weak supposal of our worth,
Or thinking by our late dear brother's death
Our state to be disjoint and out of frame,
Colleagued with the dream of his advantage,
Claudius has no internal dreams, no altrustic goals. He doesn't dream of being just or honest. Why would he? He's a murderer, an adulterer, a symbol of incest. Here's what Claudius doesn't dream about: others, namely Hamlet (his immediate enemy). Speaking to Rosencrantz and Guildenstern, he says:
Something have you heard
Of Hamlet's transformation; so call it,
Sith nor the exterior nor the inward man
Resembles that it was. What it should be,
More than his father's death, that thus hath put him
So much from the understanding of himself,
I cannot dream of:
He doesn't understand the motivations of others. He doesn't understand why Hamlet acts "crazy" or why he might want to kill him.
By contrast, Hamlet dreams of only the internal, only the sleeping kind of dream. In fact, Hamlet's dream imagery is about eternal sleep. It is all about death.
Notice what Hamlet says of dreams:
And in the famous soliloquy: