Something "amusing" makes you smile.
Something "hilarious" makes you laugh out loud.
Imagine a television talk show host who doesn't actually tell jokes, but has a sense of humor and a pleasant manner. He is amusing.
Imagine one of his guests who walks up to the microphone and tells a series of jokes that "has the audience in stitches," "has them rolling in the aisles," has everybody laughing and laughing. He is hilarious.