Luke 4:33-36 (ESV)
And in the synagogue there was a man who had the spirit of an unclean demon, and he cried out with a loud voice,  "Ha! What have you to do with us, Jesus of Nazareth? Have you come to destroy us? I know who you are— the Holy One of God."  But Jesus rebuked him, saying, "Be silent and come out of him!" And when the demon had thrown him down in their midst, he came out of him, having done him no harm.  And they were all amazed and said to one another, "What is this word? For with authority and power he commands the unclean spirits, and they come out!"
The demon knows who Jesus is. He knows but does not believe. The two are not exclusive, but neither are they synonymous. Jesus casts him out, and the people are astonished His mere words throw the demons out. Those who believe see the signs those who refused were denied.