Both angels and demons are spirit beings. They operate primarily in the spirit realm, but apparently have the ability to manifest themselves in the earthly realm. Jesus spoke of both 'the angels of God' (Matthew 22:30) and 'the devil and his angels' (Matthew 25:41), the later presumably being the demons.
This is a large topic and is beyond the scope of this website. You are correct that there is a lot of false teaching about angels and demons, but they do exist and we ought to learn as much as we can about them. If others would like to add their comments, they would be welcome. If you have specific follow up questions, please post them.